A308877 Expansion of e.g.f. (1 + log(1 - x))/(1 + 2*log(1 - x)).

1, 1, 5, 38, 386, 4904, 74776, 1330272, 27046848, 618653280, 15723024864, 439559609664, 13405656582336, 442915145716224, 15759326934391296, 600783539885546496, 24430204949876794368, 1055516761826050203648, 48286612866726631489536, 2331682676308057000255488

Offset: 0

Author

Ilya Gutkovskiy, Jun 29 2019

Keywords

• nonn

Crossrefs

Cf. A001710, A002866, A008275, A011782, A050351, A088500, A320349, A308878.

Programs

Mathematica

nmax = 19; CoefficientList[Series[(1 + Log[1 - x])/(1 + 2 Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[Sum[Abs[StirlingS1[n, k]] 2^(k - 1) k!, {k, 1, n}], {n, 1, 19}]]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} |Stirling1(n,k)| * 2^(k-1) * k!.

a(n) ~ n! * exp(n/2) / (4 * (exp(1/2) - 1)^(n+1)). - Vaclav Kotesovec, Jun 29 2019