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0]"}]}],"used_by":[],"used_by_total":0,"links":[],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:            324,             1656,              2116;\n  1:           5832,            44712,            114264,              97336;\n  2:         104976,          1073088,           4113504,            7008192,            4477456;\n  3:        1889568,         24144480,         123405120,          315368640,          402971040,           205962976;\n  4:       34012224,        521520768,        3331938240,        11353271040,        21760436160,         22244001408,          9474296896;\n  5:      612220032,      10951936128,       83964843648,       357628037760,       913938318720,       1401372088704,       1193761408896,         435817657216;\n  6:    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2116*x^2.","mathematica":"P[0, x_] := 324 + 1656*x + 2116*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((18 + 64*x + 46*x^2)*P[n - 1, x])/(1 + x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 324 + 1656*x + 2116*x^2; for(n = 1, N, my(i = n + 1); v[i] = ((18 + 64*x + 46*x^2)*v[i - 1])/(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}}],"derivation":{"root":"n-7dcf11eddf2b9a8a","steps":["basis A013611","x \u21a6 x/(x+1)"],"edges":["e-e460f89b751823ed","e-6da56fae505b5199"],"text":"A038321 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)"},"headline":"A038321 \u2192 basis A013611 \u2192 x \u21a6 x/(x+1)","chain":null}