A352326 Expansion of e.g.f.: 1/(2 - exp(x) - sinh(x)).

1, 2, 9, 62, 567, 6482, 88929, 1423382, 26037027, 535813802, 12251630349, 308153112302, 8455276083087, 251333936555522, 8045613346221369, 275950004166050822, 10095559110771678747, 392427366313299119642, 16151459739717643489989

Offset: 0

Author

Seiichi Manyama, Mar 12 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..395

Crossrefs

Cf. A000670, A006154, A028296, A094088, A352327, A352617.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-k)*binomial(n, k)*(1+(k mod 2)), k=1..n))
    end:
seq(a(n), n=0..18); # Alois P. Heinz, Mar 25 2022

Mathematica

m = 18; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - Sinh[x]), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-sinh(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(7) * log((2 + sqrt(7))/3)^(n+1)). - Vaclav Kotesovec, Mar 12 2022