A357265 Expansion of e.g.f. -LambertW(x * log(1-x)).

0, 0, 2, 3, 32, 150, 1884, 16380, 249808, 3255336, 59596560, 1037413080, 22432698144, 486784686960, 12233449250736, 316660035739320, 9111729094222080, 273147758526888000, 8880267446524694016, 301952732236006556160, 10963551960785051470080

Offset: 0

Author

Seiichi Manyama, Sep 21 2022

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A052807, A355842, A357267.

Programs

PARI

my(N=20, x='x+O('x^N)); concat([0, 0], Vec(serlaplace(-lambertw(x*log(1-x)))))

PARI

a(n) = n!*sum(k=1, n\2, k^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);

Formula

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