A349105 Expansion of e.g.f. 1/(1 - (sinh(x) + x*cosh(x))/2 ).

1, 1, 2, 8, 40, 243, 1796, 15502, 152608, 1690613, 20814208, 281859540, 4163795648, 66636761575, 1148477490304, 21207704998010, 417728195909632, 8742243282090153, 193720478508563456, 4531158728871170080, 111562803180301643776, 2884156736234559267611

Offset: 0

Author

Seiichi Manyama, Mar 26 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..435

Crossrefs

Cf. A006154, A205571, A349104, A351937.

Programs

Mathematica

With[{m = 21}, Range[0, m]! * CoefficientList[Series[1/(1 - (Sinh[x] + x*Cosh[x])/2), {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-(sinh(x)+x*cosh(x))/2)))

PARI

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

Formula

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