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v[1] = 1; v[2] = 4 + x; for(n = 2, N, my(i = n + 1); v[i] = -(2*n^2 - 2*n)*v[i - 2] + (3*n + 1 + x)*v[i - 1] + x*deriv(v[i - 1], x)); 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":"A079621","target":"triangle","first_row":0,"oeis_offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n   1:          1;\n   2:          4,          1;\n   3:         24,         12,          1;\n   4:        192,        144,         24,         1;\n   5:       1920,       1920,        480,        40,         1;\n   6:      23040,      28800,       9600,      1200,        60,        1;\n   7:     322560,     483840,     201600,     33600,      2520,       84,      1;\n   8:    5160960,    9031680,    4515840,    940800,     94080,     4704,    112,     1;\n   9:   92897280,  185794560,  108380160,  27095040,   3386880,   225792,   8064,   144,   1;\n  10: 1857945600, 4180377600, 2786918400, 812851200, 121927680, 10160640, 483840, 12960, 180, 1;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -(2*n^2-6*n+4)*P(n-2,x) + (3*n-2+x)*P(n-1,x) + x*d/dx P(n-1,x) for n >= 3, with P(1,x) = 1, P(2,x) = 4 + x.","mathematica":"P[1, x_] := 1;\nP[2, x_] := 4 + x;\nP[n_, x_] := P[n, x] = Expand[-(2*n^2 - 6*n + 4)*P[n - 2, x] + (3*n - 2 + x)*P[n - 1, x] + x*D[P[n - 1, x], x]];\nTable[PadRight[CoefficientList[P[n, x], x], n], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1; v[2] = 4 + x; for(n = 3, N, my(i = n); v[i] = -(2*n^2 - 6*n + 4)*v[i - 2] + (3*n - 2 + x)*v[i - 1] + x*deriv(v[i - 1], x)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n - #c)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i, v[i])))};\nT(10)","reading":{"first_row":0,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-6ace63f6e12c5046","steps":["basis A008277"],"edges":["e-944c70f84abc9f7e"],"text":"A079638 \u2192 basis A008277"},"headline":"A079638 \u2192 basis A008277","chain":null}