A362700 Expansion of e.g.f. 1/(1 + LambertW(-x * exp(x^2/2))).

1, 1, 4, 30, 304, 3950, 62736, 1177288, 25489024, 625404060, 17149867840, 519779815016, 17253698140416, 622521514670536, 24257636227003648, 1015256151136695840, 45421939756667293696, 2163253599528596482832, 109270502354027312243712

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^(n-k) / (2^k * k! * (n-2*k)!).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-x*exp(x^2/2)))))

Crossrefs

Cf. A072034, A362701.

Sequence in context: A379190 A307905 A292629 * A088794 A239841 A145348

Adjacent sequences: A362697 A362698 A362699 * A362701 A362702 A362703

Keyword

nonn

Author

Seiichi Manyama, Apr 30 2023

Status

approved