A009227 Expansion of e.g.f.: exp(sinh(x))/exp(x).

1, 0, 0, 1, 0, 1, 10, 1, 56, 281, 246, 4621, 16412, 53197, 564642, 1937937, 13309648, 100397649, 454215214, 4082253589, 26498068420, 174791970677, 1575851086778, 10628056916313, 91523101970104, 788580099169337, 6237722665351750, 60190551618214941

Offset: 0

Author

R. H. Hardin

Keywords

• nonn
• easy

Comments

Number of partitions of n-set in which block sizes are odd and greater than 1. - Vladeta Jovovic, Aug 23 2007

Crossrefs

Cf. A003724, A009209.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n-1, 2*j)*a(n-2*j-1), j=1..(n-1)/2))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 09 2022

Mathematica

With[{nn=30},CoefficientList[Series[Exp[Sinh[x]]/Exp[x],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 18 2015 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(sinh(x))/exp(x))) \\ Michel Marcus, Apr 09 2022

Formula

a(0) = 1; a(n) = Sum_{k=1..floor((n-1)/2)} binomial(n-1,2*k) * a(n-2*k-1). - Ilya Gutkovskiy, Apr 09 2022

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Jan 18 2015