A354518 Expansion of e.g.f. cosh(x)^exp(x).

1, 0, 1, 3, 7, 30, 166, 798, 4117, 27660, 196756, 1328448, 9866407, 86205210, 759842266, 6460661028, 60841732777, 651349676280, 6795873687496, 67981177154688, 770224145659627, 9854500496860470, 116983085896035646, 1301594922821009028, 17440543467561038557

Offset

0,4

Comments

a(39) is negative. - Vaclav Kotesovec, Aug 17 2022

Links

Seiichi Manyama, Table of n, a(n) for n = 0..486

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A354520(k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(cosh(x)^exp(x)))
(PARI) a354520(n) = sum(k=1, n\2, (16^k-4^k)*bernfrac(2*k)/(2*k)*binomial(n, 2*k));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a354520(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A000248, A003727, A215518, A354517, A354520.

Sequence in context: A132105 A019021 A110505 * A009128 A053648 A138862

Adjacent sequences: A354515 A354516 A354517 * A354519 A354520 A354521

Keyword

sign

Author

Seiichi Manyama, Aug 16 2022

Status

approved