%I #10 Jul 01 2015 08:41:45

%S 1,1,1,5,8,42,117,541,2403,10485,65778,282262,2284493,9977853,

%T 97315935,450358629,4966934284,25167390922,298399576813,1693380647429,

%U 20784317362947,134137856170593,1658511579778364,12262539123056548,150144857708406161,1273792249691584593

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

%H Alois P. Heinz, <a href="/A130223/b130223.txt">Table of n, a(n) for n = 0..500</a>

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

%p with(combinat):

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(

%p `if`(j=0 or irem(i, 2)=0 or irem(j, 2)=1, multinomial(

%p n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))

%p end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Mar 08 2015

%t 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 *)

%Y Cf. A102759.

%K easy,nonn

%O 0,4

%A _Vladeta Jovovic_, Aug 05 2007, Aug 05 2007

%E More terms from _Max Alekseyev_, Jan 31 2010