A352327 Expansion of e.g.f.: 1/(3 - exp(x) - cosh(x)).

1, 1, 4, 19, 130, 1081, 10894, 127639, 1711210, 25798141, 432212134, 7964801659, 160121522290, 3487254825601, 81790592435374, 2055350489070079, 55093108433421370, 1569052795651631461, 47315282424232826614, 1506074331671551028899

Offset: 0

Author

Seiichi Manyama, Mar 12 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..414

Crossrefs

Cf. A000670, A006154, A094088, A352326, A352624.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-k)*binomial(n, k)*(2-(k mod 2)), k=1..n))
    end:
seq(a(n), n=0..19); # Alois P. Heinz, Mar 25 2022

Mathematica

m = 19; Range[0, m]! * CoefficientList[Series[1/(3 - Exp[x] - Cosh[x]), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(3-exp(x)-cosh(x))))

PARI

a(n) = if(n==0, 1, sum(k=1, n, (3+(-1)^k)/2*binomial(n, k)*a(n-k)));

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (3+(-1)^k)/2 * binomial(n,k) * a(n-k).

a(n) ~ n! / (sqrt(6) * log(1 + sqrt(2/3))^(n+1)). - Vaclav Kotesovec, Mar 12 2022