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v[1] = 2; v[2] = 13 + 13*x; v[3] = 2 + 334*x + 2*x^2; for(n = 4, N, my(i = n); v[i] = ((n - 3 + (n - 3)*x)*v[i - 1] + (143*n - 429)*x*v[i - 2])/(n - 3)); 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}},{"oeis_id":"A153651","target":"reversed_triangle","first_row":0,"oeis_offset":1,"reversed":true,"trim_zeros":"none","regular_triangle":true,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n   1:  2;\n   2: 13,   13;\n   3:  2,  334,       2;\n   4:  2, 2195,    2195,         2;\n   5:  2, 2483,   52152,      2483,           2;\n   6:  2, 2771,  368520,    368520,        2771,           2;\n   7:  2, 3059,  726360,   8194776,      726360,        3059,         2;\n   8:  2, 3347, 1125672,  61619496,    61619496,     1125672,      3347,       2;\n   9:  2, 3635, 1566456, 166614648,  1295091960,   166614648,   1566456,    3635,    2;\n  10:  2, 3923, 2048712, 329152200, 10273294536, 10273294536, 329152200, 2048712, 3923, 2;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where (n-3)*P(n,x) = (n-3+(n-3)*x)*P(n-1,x) + (143*n-429)*x*P(n-2,x) for n >= 4, with P(1,x) = 2, P(2,x) = 13 + 13*x, P(3,x) = 2 + 334*x + 2*x^2.","mathematica":"P[1, x_] := 2;\nP[2, x_] := 13 + 13*x;\nP[3, x_] := 2 + 334*x + 2*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((n - 3 + (n - 3)*x)*P[n - 1, x] + (143*n - 429)*x*P[n - 2, x])/(n - 3)]];\nTable[Reverse[PadRight[CoefficientList[P[n, x], x], n]], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 2; v[2] = 13 + 13*x; v[3] = 2 + 334*x + 2*x^2; for(n = 4, N, my(i = n); v[i] = ((n - 3 + (n - 3)*x)*v[i - 1] + (143*n - 429)*x*v[i - 2])/(n - 3)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n - #c)); c = Vecrev(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":true,"trim_zeros":"none","regular_triangle":true}}],"derivation":{"root":"n-2a67b0774691ba3b","steps":[],"edges":[],"text":"A153651"},"headline":"A153651: Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + (j+5)*prime(j)*T(n-2, k-1) with j=6, read by rows.","chain":null}