A337060 E.g.f.: 1 / (1 + x^2/2 + log(1 - x)).

1, 1, 2, 8, 46, 324, 2708, 26424, 295272, 3714600, 51929472, 798610416, 13399081584, 243556758912, 4767863027328, 100004300847744, 2237419620187776, 53187370914349440, 1338737435337261312, 35568441673932566016, 994744655047298951424, 29211127285363209561600

Offset: 0

Author

Ilya Gutkovskiy, Aug 13 2020

Keywords

• nonn

Crossrefs

Cf. A000266, A007840, A226226, A337061.

Programs

Mathematica

nmax = 21; CoefficientList[Series[1/(1 + x^2/2 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] (k - 1)! a[n - k], {k, 3, n}]; Table[a[n], {n, 0, 21}]

Formula

a(0) = 1; a(n) = n * a(n-1) + Sum_{k=3..n} binomial(n,k) * (k-1)! * a(n-k).