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in other words, the unsigned Stirling numbers of the first kind in reverse order).","first_index":0,"fingerprint":"f6-34eaf45657600f7a","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["1","1"],["1","3","2"]],"card_rows":[["1"],["1","1"],["1","3","2"],["1","6","11","6"]],"row_sums_preview":["1","2","6","24","120","720","5040","40320"],"regions":["(-inf, 0)","(-inf, 0]"],"region_exact":{},"oeis_ids":["A094638"],"derivation":{"root":"n-4d60c3dd8627c01d","steps":[],"edges":[],"text":"A094638"},"headline":"A094638: Triangle read by rows: T(n,k) = |s(n,n+1-k)|, where s(n,k) are the signed Stirling numbers of the first kind A008276 (1 <= k <= n; in other words, the unsigned Stirling numbers of the first kind in reverse order).","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:                1;\n  1:                2,                 2;\n  2:               24,                36,                12;\n  3:              720,              1320,               720,               120;\n  4:            40320,             84000,             58800,             16800,             1680;\n  5:          3628800,           8285760,           6804000,           2570400,           453600,            30240;\n  6:        479001600,        1173553920,        1080414720,         488980800,        116424000,         13970880,          665280;\n  7:      87178291200,      226040855040,      227147880960,      117085288320,      33902668800,       5569724160,       484323840,       17297280;\n  8:   20922789888000,    56865153945600,    61296717081600,    34914905625600,   11649199161600,    2353813862400,    283329446400,    18681062400,    518918400;\n  9: 6402373705728000, 18112111963545600, 20690210661120000, 12768049502208000, 4751761734720000, 1116339813388800, 166728481920000, 15349606272000, 793945152000, 17643225600;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (4*n^2-2*n+(4*n-2)*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(4*n^2 - 2*n + (4*n - 2)*x)*P[n - 1, x]];\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] = (4*n^2 - 2*n + (4*n - 2)*x)*v[i - 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-1336d058dca9979e","steps":["basis A007318","basis A013609"],"edges":["e-857dad5fd144a15f","e-06c6504439f9fc2a"],"text":"A204420 \u2192 basis A007318 \u2192 basis A013609"},"headline":"A204420 \u2192 basis A007318 \u2192 basis A013609","chain":null}