A102759 Number of partitions of n-set in which number of blocks of size 2k is even (or zero) for every k.

1, 1, 1, 2, 8, 27, 82, 338, 1647, 7668, 37779, 210520, 1276662, 7985200, 51302500, 358798144, 2677814900, 20309850311, 160547934756, 1344197852830, 11666610870142, 104156661915427, 962681713955130, 9238216839975106, 91508384728188792, 930538977116673878

Offset

0,4

Links

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

Formula

E.g.f. for offset 2: exp(sinh(x))*Product_{k>=1} cosh(x^(2*k)/(2*k)!). - Geoffrey Critzer, Jan 02 2011

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       add(`if`(irem(i, 2)=1 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(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] == 1 || Mod[j, 2] == 0, multinomial[n, Join[{n-i*j}, Table[i, {j}]]]/j!*b[n-i*j, i-1], 0], {j, 0, n/i}]]] ; a[n_] := b[n, n]; Table[ a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 16 2015, after Alois P. Heinz *)

Prog

(PARI) N=31; x='x+O('x^N);
Vec(serlaplace(exp(sinh(x))*prod(k=1, N, cosh(x^(2*k)/(2*k)!))))
/* gives: [1, 1, 1, 2, 8, 27, 82, 338, 1647, 7668, ...] , Joerg Arndt, Jan 03 2011 */

Crossrefs

Cf. A003483, A006950, A130219 - A130223.

Sequence in context: A289864 A290056 A100505 * A292698 A261056 A295135

Adjacent sequences: A102756 A102757 A102758 * A102760 A102761 A102762

Keyword

nonn

Author

Vladeta Jovovic, Feb 10 2005, Aug 05 2007

Extensions

Offset changed to 0 and two 1's prepended by Alois P. Heinz, Mar 08 2015

Status

approved