A380155 Expansion of e.g.f. 1/sqrt(1 - 2*x*exp(2*x)).

1, 1, 7, 63, 785, 12545, 244407, 5619775, 148977313, 4473497601, 150078670055, 5563415292479, 225832882678449, 9962766560986369, 474619650950131351, 24283168467229957695, 1327993894505461755713, 77305844496338607597569, 4772660185400974888323015

Offset

0,3

Links

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

Formula

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

a(n) == 1 (mod 2).

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

Prog

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

Crossrefs

Cf. A006153, A380156.

Cf. A380014, A380015.

Sequence in context: A346683 A084063 A184141 * A349720 A376324 A152797

Adjacent sequences: A380152 A380153 A380154 * A380156 A380157 A380158

Keyword

nonn

Author

Seiichi Manyama, Jan 13 2025

Status

approved