A357267 Expansion of e.g.f. -LambertW(x * (1 - exp(x))).

0, 0, 2, 3, 28, 125, 1506, 12607, 186600, 2352681, 41839750, 705821171, 14818593516, 311784460429, 7603945309338, 190868446707135, 5328147004384336, 154893585657590609, 4884408906341245326, 161057122218190660555, 5671407469802947722900

Offset: 0

Author

Seiichi Manyama, Sep 21 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A048802, A355843, A357265.

Programs

PARI

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

PARI

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

Formula

a(n) = n! * Sum_{k=1..floor(n/2)} k^(k-1) * Stirling2(n-k,k)/(n-k)!.