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

0,4

Links

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

Formula

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

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 *)

Crossrefs

Cf. A102759.

Sequence in context: A192272 A073930 A342021 * A126750 A256401 A109292

Adjacent sequences: A130220 A130221 A130222 * A130224 A130225 A130226

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 05 2007, Aug 05 2007

Extensions

More terms from Max Alekseyev, Jan 31 2010

Status

approved