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v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":true}},{"oeis_id":"A257611","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:     3,       3;\n  2:     9,      30,         9;\n  3:    27,     213,       213,         27;\n  4:    81,    1308,      2982,       1308,         81;\n  5:   243,    7431,     32646,      32646,       7431,        243;\n  6:   729,   40314,    310263,     587628,     310263,      40314,        729;\n  7:  2187,  212505,   2695923,    8701545,    8701545,    2695923,     212505,      2187;\n  8:  6561, 1099704,  22059036,  113360904,  191433990,  113360904,   22059036,   1099704,    6561;\n  9: 19683, 5623179, 173108220, 1351133676, 3579465642, 3579465642, 1351133676, 173108220, 5623179, 19683;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where P(n,x) = (3+(2*n+1)*x)*P(n-1,x) + (2*x-2*x^2)*d/dx P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(3 + (2*n + 1)*x)*P[n - 1, x] + (2*x - 2*x^2)*D[P[n - 1, x], 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] = (3 + (2*n + 1)*x)*v[i - 1] + (2*x - 2*x^2)*deriv(v[i - 1], x)); 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-0c0e99d973615582","steps":[],"edges":[],"text":"A257611"},"headline":"A257611: Triangle, read by rows, T(n,k) = t(n-k, k) where t(n,m) = f(m)*t(n-1,m) + 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