A294191 a(n) = n! * [x^n] exp(n*((1+x)^n - 1)).

1, 1, 20, 1233, 152416, 31391225, 9694519776, 4190408587645, 2414572869757952, 1788571346467193361, 1655904985345402048000, 1873608841984994237091881, 2543757905332880336197324800, 4081324788082969930056684134953, 7639334000918272184846041849942016

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..209

Formula

a(n) ~ n^(2*n) / (sqrt(1 + LambertW(1)) * exp(n*(2 - 1/LambertW(1))) * LambertW(1)^(n - 1/2)). - Vaclav Kotesovec, Feb 11 2026

Crossrefs

Main diagonal of A294118.

Cf. A294045.

Sequence in context: A363054 A158912 A036067 * A359645 A001451 A093598

Adjacent sequences: A294188 A294189 A294190 * A294192 A294193 A294194

Keyword

nonn

Author

Seiichi Manyama, Oct 24 2017

Status

approved