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begins:\n  0: 1;\n  1: 2,  1;\n  2: 2,  3,  1;\n  3: 2,  5,  4,   1;\n  4: 2,  7,  9,   5,   1;\n  5: 2,  9, 16,  14,   6,   1;\n  6: 2, 11, 25,  30,  20,   7,   1;\n  7: 2, 13, 36,  55,  50,  27,   8,  1;\n  8: 2, 15, 49,  91, 105,  77,  35,  9,  1;\n  9: 2, 17, 64, 140, 196, 182, 112, 44, 10, 1;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (n-1+(n-1)*x)*P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 2 + x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 2 + x;\nP[n_, x_] := P[n, x] = Expand[Together[((n - 1 + (n - 1)*x)*P[n - 1, x])/(n - 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 2 + x; for(n = 2, N, my(i = n + 1); v[i] = ((n - 1 + (n - 1)*x)*v[i - 1])/(n - 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":"A029653","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: 2,  1;\n  2: 2,  3,  1;\n  3: 2,  5,  4,   1;\n  4: 2,  7,  9,   5,   1;\n  5: 2,  9, 16,  14,   6,   1;\n  6: 2, 11, 25,  30,  20,   7,   1;\n  7: 2, 13, 36,  55,  50,  27,   8,  1;\n  8: 2, 15, 49,  91, 105,  77,  35,  9,  1;\n  9: 2, 17, 64, 140, 196, 182, 112, 44, 10, 1;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (n-1+(n-1)*x)*P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 2 + x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 2 + x;\nP[n_, x_] := P[n, x] = Expand[Together[((n - 1 + (n - 1)*x)*P[n - 1, x])/(n - 1)]];\nTable[PadRight[CoefficientList[P[n, x], x], n + 1], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 2 + x; for(n = 2, N, my(i = n + 1); v[i] = ((n - 1 + (n - 1)*x)*v[i - 1])/(n - 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}}],"derivation":{"root":"n-2c5f5be79d9d1ae3","steps":[],"edges":[],"text":"A029653"},"headline":"A029653: Numbers in (2,1)-Pascal triangle (by row).","chain":null}