A337061 E.g.f.: 1 / (1 + x^3/3 + log(1 - x)).

1, 1, 3, 12, 72, 534, 4818, 50532, 606408, 8182656, 122712912, 2024328096, 36432644400, 710346495312, 14915647605168, 335567743462944, 8052843408926976, 205328108580310656, 5543345188496499840, 157970863597032124416, 4738694884696030305024

Offset: 0

Author

Ilya Gutkovskiy, Aug 13 2020

Keywords

• nonn

Crossrefs

Cf. A000090, A007840, A226226, A337060.

Programs

Mathematica

nmax = 20; CoefficientList[Series[1/(1 + x^3/3 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = a[1] = 1; a[n_] := a[n] = n (a[n - 1] + (n - 1) a[n - 2]/2) + Sum[Binomial[n, k] (k - 1)! a[n - k], {k, 4, n}]; Table[a[n], {n, 0, 20}]

Formula

a(0) = a(1) = 1; a(n) = n * (a(n-1) + (n-1) * a(n-2) / 2) + Sum_{k=4..n} binomial(n,k) * (k-1)! * a(n-k).