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17788815,      8696754,      1771561;\n  7:   4782969,   40920957,   150043509,   305644185,    373565115,    273947751,    111608343,    19487171;\n  8:  43046721,  420901272,  1800522108,  4401276264,   6724172070,   6574746024,   4017900348,  1403076312,   214358881;\n  9: 387420489, 4261625379, 20834612964, 59417229564, 108931587534, 133138606986, 108483309396, 56824590636, 17363069361, 2357947691;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (11+9*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 + 9*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 + 9*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}},{"oeis_id":"A038323","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,           9;\n  2:        121,         198,          81;\n  3:       1331,        3267,        2673,          729;\n  4:      14641,       47916,       58806,        32076,         6561;\n  5:     161051,      658845,     1078110,       882090,       360855,        59049;\n  6:    1771561,     8696754,    17788815,     19405980,     11908215,      3897234,      531441;\n  7:   19487171,   111608343,   273947751,    373565115,    305644185,    150043509,    40920957,     4782969;\n  8:  214358881,  1403076312,  4017900348,   6574746024,   6724172070,   4401276264,  1800522108,   420901272,   43046721;\n  9: 2357947691, 17363069361, 56824590636, 108483309396, 133138606986, 108931587534, 59417229564, 20834612964, 4261625379, 387420489;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (11+9*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 + 9*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 + 9*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}}],"derivation":{"root":"n-4e096b5929fd3f2e","steps":[],"edges":[],"text":"A038323"},"headline":"A038323: Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*9^j.","chain":null}