A130223 Number of partitions of n-set in which number of blocks of size 2k-1 is odd (or zero) for every k.

1, 1, 1, 5, 8, 42, 117, 541, 2403, 10485, 65778, 282262, 2284493, 9977853, 97315935, 450358629, 4966934284, 25167390922, 298399576813, 1693380647429, 20784317362947, 134137856170593, 1658511579778364, 12262539123056548, 150144857708406161, 1273792249691584593

Offset: 0

Author

Vladeta Jovovic, Aug 05 2007, Aug 05 2007

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A102759.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      `if`(j=0 or irem(i, 2)=0 or irem(j, 2)=1, multinomial(
       n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 08 2015

Mathematica

max = 26; f[x_] = Exp[Cosh[x]-1]*Product[1+Sinh[x^(2*k-1)/(2*k-1)!], {k, 0, max}]; CoefficientList[f[x] + O[x]^max, x]*Range[0, max-1]! (* Jean-François Alcover, Jul 01 2015 *)

Formula

E.g.f.: exp(cosh(x)-1)*Product_{k>0} (1+sinh(x^(2*k-1)/(2*k-1)!)).

Extensions

More terms from Max Alekseyev, Jan 31 2010