A380014 Expansion of e.g.f. 1/sqrt(exp(-2*x) - 2*x).

1, 2, 10, 88, 1084, 17176, 332824, 7623904, 201540112, 6038820640, 202246657696, 7486877795200, 303561658686400, 13378863292503424, 636833910410881408, 32559375816074384896, 1779494669204225605888, 103532173699456380625408, 6388705590982575700625920

Offset

0,2

Links

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

Formula

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

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

Prog

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

Crossrefs

Cf. A072597, A380016, A380018.

Sequence in context: A245009 A379932 A354240 * A306404 A111811 A186448

Adjacent sequences: A380011 A380012 A380013 * A380015 A380016 A380017

Keyword

nonn

Author

Seiichi Manyama, Jan 09 2025

Status

approved