A370084 Expansion of e.g.f. exp( Sum_{k>=1} (2*k)! * (x/2)^k/k ).

1, 1, 7, 199, 15985, 2810401, 916442551, 497173378087, 416055798439009, 508038355486018945, 867346995542879712871, 2001283948891590010467271, 6070787760933663329315253457, 23660956435620796919900079644449

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (2*k)!*(x/2)^k/k))))

Crossrefs

Cf. A158876, A370085.

Cf. A370086.

Sequence in context: A206473 A376461 A300616 * A178319 A202943 A355088

Adjacent sequences: A370081 A370082 A370083 * A370085 A370086 A370087

Keyword

nonn

Author

Seiichi Manyama, Feb 08 2024

Status

approved