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begins:\n 0: 1;\n 1: 11, 11;\n 2: 121, 242, 121;\n 3: 1331, 3993, 3993, 1331;\n 4: 14641, 58564, 87846, 58564, 14641;\n 5: 161051, 805255, 1610510, 1610510, 805255, 161051;\n 6: 1771561, 10629366, 26573415, 35431220, 26573415, 10629366, 1771561;\n 7: 19487171, 136410197, 409230591, 682050985, 682050985, 409230591, 136410197, 19487171;\n 8: 214358881, 1714871048, 6002048668, 12004097336, 15005121670, 12004097336, 6002048668, 1714871048, 214358881;\n 9: 2357947691, 21221529219, 84886116876, 198067606044, 297101409066, 297101409066, 198067606044, 84886116876, 21221529219, 2357947691;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (11+11*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(11 + 11*x)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = (11 + 11*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}},{"oeis_id":"A038325","target":"triangle","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n 0: 1;\n 1: 11, 11;\n 2: 121, 242, 121;\n 3: 1331, 3993, 3993, 1331;\n 4: 14641, 58564, 87846, 58564, 14641;\n 5: 161051, 805255, 1610510, 1610510, 805255, 161051;\n 6: 1771561, 10629366, 26573415, 35431220, 26573415, 10629366, 1771561;\n 7: 19487171, 136410197, 409230591, 682050985, 682050985, 409230591, 136410197, 19487171;\n 8: 214358881, 1714871048, 6002048668, 12004097336, 15005121670, 12004097336, 6002048668, 1714871048, 214358881;\n 9: 2357947691, 21221529219, 84886116876, 198067606044, 297101409066, 297101409066, 198067606044, 84886116876, 21221529219, 2357947691;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (11+11*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(11 + 11*x)*P[n - 1, x]];\nTable[PadRight[CoefficientList[P[n, x], x], n + 1], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = (11 + 11*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":true}},{"oeis_id":"A038325","target":"reversed_triangle","first_row":0,"oeis_offset":0,"reversed":true,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n 0: 1;\n 1: 11, 11;\n 2: 121, 242, 121;\n 3: 1331, 3993, 3993, 1331;\n 4: 14641, 58564, 87846, 58564, 14641;\n 5: 161051, 805255, 1610510, 1610510, 805255, 161051;\n 6: 1771561, 10629366, 26573415, 35431220, 26573415, 10629366, 1771561;\n 7: 19487171, 136410197, 409230591, 682050985, 682050985, 409230591, 136410197, 19487171;\n 8: 214358881, 1714871048, 6002048668, 12004097336, 15005121670, 12004097336, 6002048668, 1714871048, 214358881;\n 9: 2357947691, 21221529219, 84886116876, 198067606044, 297101409066, 297101409066, 198067606044, 84886116876, 21221529219, 2357947691;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (11+11*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(11 + 11*x)*P[n - 1, x]];\nTable[Reverse[PadRight[CoefficientList[P[n, x], x], n + 1]], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = (11 + 11*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c = Vecrev(c); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":true,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-8064e72cf80883a7","steps":[],"edges":[],"text":"A038325"},"headline":"A038325: Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*11^j.","chain":null}