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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..500
Programs
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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 *) -
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 */
Formula
E.g.f. for offset 2: exp(sinh(x))*Product_{k>=1} cosh(x^(2*k)/(2*k)!). - Geoffrey Critzer, Jan 02 2011
Extensions
Offset changed to 0 and two 1's prepended by Alois P. Heinz, Mar 08 2015