A308878 Expansion of e.g.f. (1 - log(1 + x))/(1 - 2*log(1 + x)).

1, 1, 3, 14, 86, 664, 6136, 66240, 816672, 11331552, 174662304, 2961774144, 54785368128, 1097882522112, 23693117756928, 547844658441216, 13511950038494208, 354086653712228352, 9824794572366544896, 287752569360558907392, 8871374335098501292032

Offset

0,3

Comments

Inverse Stirling transform of A002866.

Links

Table of n, a(n) for n=0..20.

Formula

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

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

Mathematica

nmax = 20; CoefficientList[Series[(1 - Log[1 + x])/(1 - 2 Log[1 + x]), {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[Sum[StirlingS1[n, k] 2^(k - 1) k!, {k, 1, n}], {n, 1, 20}]]

Crossrefs

Cf. A002866, A008275, A011782, A050351, A088501, A306042, A308877.

Sequence in context: A127715 A307440 A087912 * A051818 A091102 A323771

Adjacent sequences: A308875 A308876 A308877 * A308879 A308880 A308881

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 29 2019

Status

approved