A380639 Expansion of e.g.f. exp(x/(1 - 2*x)^2).

1, 1, 9, 97, 1297, 20961, 398041, 8678209, 213337377, 5830560577, 175187949481, 5734893998241, 203021979225649, 7724154592735777, 314158263983430777, 13597375157683820161, 623802598335834369601, 30228101725367033318529, 1542430410234859308052297

Offset

0,3

Links

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

Formula

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

E.g.f.: exp( Sum_{k>=1} k * 2^(k-1) * x^k ).

a(n) ~ 2^n * n^(n - 1/6) / (sqrt(3) * exp(n - 3*n^(2/3)/2 + 1/24)). - Vaclav Kotesovec, Jan 29 2025

Prog

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

Crossrefs

Cf. A380636, A380640.

Cf. A082579.

Sequence in context: A194725 A218500 A293986 * A123821 A145509 A098782

Adjacent sequences: A380636 A380637 A380638 * A380640 A380641 A380642

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 28 2025

Status

approved