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A007318","chain":null}}],"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:        0;\n  1:       16;\n  2:      160,        512;\n  3:     1200,       7680,       12288;\n  4:     8000,      76800,      245760,       262144;\n  5:    50000,     640000,     3072000,      6553600,      5242880;\n  6:   300000,    4800000,    30720000,     98304000,    157286400,     100663296;\n  7:  1750000,   33600000,   268800000,   1146880000,   2752512000,    3523215360,    1879048192;\n  8: 10000000,  224000000,  2150400000,  11468800000,  36700160000,   70464307200,   75161927680,   34359738368;\n  9: 56250000, 1440000000, 16128000000, 103219200000, 412876800000, 1056964608000, 1691143372800, 1546188226560, 618475290624;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (5*n+16*n*x)*P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 16.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 16;\nP[n_, x_] := P[n, x] = Expand[Together[((5*n + 16*n*x)*P[n - 1, x])/(n - 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 0; v[2] = 16; for(n = 2, N, my(i = n + 1); v[i] = ((5*n + 16*n*x)*v[i - 1])/(n - 1)); 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-2e0409c0014ec240","steps":["basis A013611","D"],"edges":["e-189a8da608edbb49","e-06ab74b4c5a19422"],"text":"A013611 \u2192 basis A013611 \u2192 D"},"headline":"A013611 \u2192 basis A013611 \u2192 D","chain":null}