A376327 Expansion of e.g.f. -LambertW(-x/(1-x^2)).

0, 1, 2, 15, 112, 1285, 17616, 299299, 5946368, 136497897, 3544641280, 102858065431, 3297199331328, 115730076038317, 4414151526557696, 181797547951527915, 8040649885153755136, 380100842138029431121, 19125314442962053300224, 1020539634854353310016415, 57563650890815727219507200

Offset

0,3

Links

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

Formula

a(n) ~ (1 + 4*exp(-2))^(1/4) * 2^n * n^(n-1) / (exp(n) * (sqrt(4 + exp(2)) - exp(1))^n).

Mathematica

nmax=25; CoefficientList[Series[-LambertW[-x/(1-x^2)], {x, 0, nmax}], x] * Range[0, nmax]!

Crossrefs

Cf. A052871, A376106.

Sequence in context: A026113 A052874 A360432 * A074622 A031507 A207998

Adjacent sequences: A376324 A376325 A376326 * A376328 A376329 A376330

Keyword

nonn

Author

Vaclav Kotesovec, Sep 20 2024

Status

approved