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v[1] = 2; v[2] = 7 + 7*x; v[3] = 2 + 94*x + 2*x^2; for(n = 4, N, my(i = n); v[i] = ((n - 3 + (n - 3)*x)*v[i - 1] + (35*n - 105)*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":"A153649","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: 7,   7;\n   3: 2,  94,     2;\n   4: 2, 341,   341,       2;\n   5: 2, 413,  3972,     413,        2;\n   6: 2, 485, 16320,   16320,      485,        2;\n   7: 2, 557, 31260,  171660,    31260,      557,       2;\n   8: 2, 629, 48792,  774120,   774120,    48792,     629,     2;\n   9: 2, 701, 68916, 1917012,  7556340,  1917012,   68916,   701,   2;\n  10: 2, 773, 91632, 3693648, 36567552, 36567552, 3693648, 91632, 773, 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) + (35*n-105)*x*P(n-2,x) for n >= 4, with P(1,x) = 2, P(2,x) = 7 + 7*x, P(3,x) = 2 + 94*x + 2*x^2.","mathematica":"P[1, x_] := 2;\nP[2, x_] := 7 + 7*x;\nP[3, x_] := 2 + 94*x + 2*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((n - 3 + (n - 3)*x)*P[n - 1, x] + (35*n - 105)*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] = 7 + 7*x; v[3] = 2 + 94*x + 2*x^2; for(n = 4, N, my(i = n); v[i] = ((n - 3 + (n - 3)*x)*v[i - 1] + (35*n - 105)*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-6db0c6ee051777e9","steps":[],"edges":[],"text":"A153649"},"headline":"A153649: Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + (j+1)*prime(j)*T(n-2, k-1) with j=4, read by rows.","chain":null}
