A380015 Expansion of e.g.f. 1/sqrt(1 - 2*x*exp(x)).

1, 1, 5, 36, 361, 4640, 72771, 1347598, 28778849, 696288888, 18823644595, 562350743306, 18397666000209, 654164843763340, 25118967828553067, 1035914449832324070, 45665488606439586241, 2142825945301659242576, 106641225471890568771747, 5610282675990428302440130

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = n! * Sum_{k=0..n} (-2)^k * k^(n-k) * binomial(-1/2,k)/(n-k)!.

a(n) ~ sqrt(2) * n^n / (sqrt(1 + LambertW(1/2)) * exp(n) * LambertW(1/2)^n). - Vaclav Kotesovec, Jan 23 2025

Prog

(PARI) a(n) = n!*sum(k=0, n, (-2)^k*k^(n-k)*binomial(-1/2, k)/(n-k)!);

Crossrefs

Cf. A006153, A380017, A380019.

Sequence in context: A031971 A247496 A302584 * A356001 A230887 A365356

Adjacent sequences: A380010 A380011 A380014 * A380016 A380017 A380018

Keyword

nonn,changed

Author

Seiichi Manyama, Jan 09 2025

Status

approved