A107403 Expansion of e.g.f. 1/(1 - 3*sinh(x)).

1, 3, 18, 165, 2016, 30783, 564048, 12057825, 294587136, 8096756763, 247266851328, 8306410495485, 304403359942656, 12085026305182743, 516690458532292608, 23668814542820609145, 1156515067746149400576, 60041982382475841900723, 3300519734382436473765888

Offset: 0

Author

Miklos Kristof, Jun 09 2005

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..379

Crossrefs

Cf. A000557, A006154, A136630.

Programs

Maple

E(x):=1/(1-3*sinh(x)): f[0]:=E(x): for n from 1 to 30 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..30);

Mathematica

CoefficientList[Series[1/(1-3*Sinh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*sinh(x)))) \\ Seiichi Manyama, Mar 26 2022

Formula

a(n) ~ n!/(sqrt(10)*(log(1/3+sqrt(10)/3))^(n+1)). - Vaclav Kotesovec, Jun 26 2013

a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} binomial(n,2*k+1) * a(n-2*k-1). - Ilya Gutkovskiy, Mar 10 2022

a(n) = Sum_{k=0..n} 3^k * k! * A136630(n,k). - Seiichi Manyama, Jun 25 2025