A355284 Expansion of e.g.f. 1 / (1 + x + x^2/2 + log(1 - x)).
1, 0, 0, 2, 6, 24, 200, 1560, 12936, 130368, 1458432, 17623440, 233922480, 3376625472, 52382131776, 870882440064, 15459372915840, 291596692838400, 5824039155720192, 122814724467223296, 2726547887891407104, 63562453551393223680, 1552499303360183700480
Offset: 0
Keywords
Programs
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Mathematica
nmax = 22; CoefficientList[Series[1/(1 + x + x^2/2 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]! a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (k - 1)! a[n - k], {k, 3, n}]; Table[a[n], {n, 0, 22}] -
PARI
my(x='x+O('x^30)); Vec(serlaplace(1/(1 + x + x^2/2 + log(1 - x)))) \\ Michel Marcus, Jun 27 2022
Formula
E.g.f.: 1 / (1 - Sum_{k>=3} x^k/k).
a(0) = 1; a(n) = Sum_{k=3..n} binomial(n,k) * (k-1)! * a(n-k).