A362911 Expansion of e.g.f. 1/( 1 - (1 + x) * log(1 + x) ).

1, 1, 3, 11, 60, 384, 3062, 27838, 293416, 3447768, 45277392, 651587760, 10254900048, 174557518992, 3203361670896, 62938642659504, 1319693558377728, 29390794198726656, 693223221342879360, 17256288944072200320, 452215395177034040064

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k) * A006153(k).

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / ((1 + LambertW(1)) * exp(n) * (1/LambertW(1) - 1)^(n+1)). - Vaclav Kotesovec, Nov 11 2023

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(1+x)*log(1+x))))

Crossrefs

Cf. A305306, A362912.

Cf. A005727, A006153, A305307.

Sequence in context: A152796 A007807 A075201 * A136440 A303871 A231344

Adjacent sequences: A362908 A362909 A362910 * A362912 A362913 A362914

Keyword

nonn

Author

Seiichi Manyama, May 10 2023

Status

approved