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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:         1;\n  1:        12,         8,          1;\n  2:       108,       168,         84,         16,           1;\n  3:       864,      2160,       2052,        936,         216,          24,           1;\n  4:      6480,     22464,      31968,      24192,       10584,        2736,         408,         32,          1;\n  5:     46656,    207360,     395280,     423360,      280800,      120096,       33480,       6000,        660,         40,         1;\n  6:    326592,   1772928,    4245696,    5909760,     5307120,     3229632,     1362528,     400896,      81540,      11160,       972,        48,        1;\n  7:   2239488,  14370048,   41477184,   71197056,    80994816,    64447488,    36913968,   15436224,    4729536,    1055376,    168588,     18648,     1344,      56,      1;\n  8:  15116544, 111974400,  378473472,  773369856,  1067302656,  1052932608,   766838016,  419945472,  174553056,   55195776,  13220928,   2370816,   311472,   28896,   1776,    64,    1;\n  9: 100776960, 846526464, 3280290048, 7779981312, 12637430784, 14908271616, 13219137792, 8997143040, 4759751808, 1970002944, 638883936, 161834112, 31752000, 4753728, 530064, 42336, 2268, 72, 1;\n","recurrence_sentence":"The row polynomials satisfy (6*n+(2*n+4)*x+x^2)*P(n,x) = (36*n+36+(48*n+72)*x+(18*n+48)*x^2+(2*n+12)*x^3+x^4)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((36*n + 36 + (48*n + 72)*x + (18*n + 48)*x^2 + (2*n + 12)*x^3 + x^4)*P[n - 1, x])/(6*n + (2*n + 4)*x + x^2)]];\nTable[CoefficientList[P[n, x], x], {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] = ((36*n + 36 + (48*n + 72)*x + (18*n + 48)*x^2 + (2*n + 12)*x^3 + x^4)*v[i - 1])/(6*n + (2*n + 4)*x + x^2)); 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-d3c3090977105807","steps":["x \u21a6 x+1","D+1"],"edges":["e-33933faab90bc4be","e-88e10245d44d5321"],"text":"A272867 \u2192 x \u21a6 x+1 \u2192 D+1"},"headline":"A272867 \u2192 x \u21a6 x+1 \u2192 D+1","chain":null}
