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A102759 Number of partitions of n-set in which number of blocks of size 2k is even (or zero) for every k. 9
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)