A130222 Number of partitions of 2n-set in which number of blocks of size 2k-1 is even (or zero) for every k.

1, 2, 11, 117, 2116, 54233, 1822053, 76771684, 3922196627, 238355654605, 16936961517144, 1387902030575371, 129757092644981529, 13704639448111317852, 1621528608322059614411, 213338281602779271672663, 31000779368619961156885708, 4945841944762007645453032073

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

Formula

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

Maple

A:= proc(n) exp(cosh(x)-1) *mul(cosh(x^(2*k-1)/ (2*k-1)!), k=1..n) end: a:= n-> coeff(series(A(n), x, 2*n+1), x, 2*n) *(2*n)!: seq(a(n), n=0..20); # Alois P. Heinz, Sep 29 2008
# second Maple program:
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      `if`(irem(i, 2)=0 or j=0 or irem(j, 2)=0, multinomial(
       n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))
    end:
a:= n-> b(2*n$2):
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 08 2015

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[If[Mod[i, 2]==0 || j==0 || Mod[j, 2]==0, multinomial[n, {n - i j} ~Join~ Table[i, {j}]]/j! b[n - i j, i-1], 0], {j, 0, n/i}]]];
a[n_] := b[2n, 2n];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 19 2020, after Alois P. Heinz *)

Crossrefs

Cf. A102759.

Sequence in context: A269082 A304639 A374140 * A197993 A057076 A346650

Adjacent sequences: A130219 A130220 A130221 * A130223 A130224 A130225

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 05 2007, Aug 05 2007

Extensions

More terms from Alois P. Heinz, Sep 29 2008

Status

approved