A130219 Number of partitions of 2n-set in which number of blocks of size k is even (or zero) for every k.

1, 1, 4, 56, 631, 15457, 582374, 18589286, 894499204, 51154344582, 3823359163826, 274722100927166, 25458967562911128, 2569179797929092506, 284554990016509385086, 37830153187190688287522, 5093072752898942262610007, 798814778335473578083666573

Offset

0,3

Links

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

Formula

E.g.f.: Product_{k>0} cosh(x^k/k!).

Example

a(2)=4 because we have ab|cd, ac|bd, ad|bc and a|b|c|d.

Maple

g:=product(cosh(x^k/factorial(k)), k=1..35): gser:=series(g, x=0, 32): seq(factorial(2*n)*coeff(gser, x, 2*n), n=0..14); # Emeric Deutsch, Sep 01 2007
# second Maple program:
g:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
     `if`(irem(j, 2)=0, g(n-i*j, i-1, p+j*i)/j!/i!^j, 0), j=0..n/i)))
    end:
a:= n-> g(2*n$2, 0):
seq(a(n), n=0..20);  # Alois P. Heinz, Mar 06 2015

Mathematica

g[n_, i_, p_] := g[n, i, p] = If[n == 0, p!, If[i<1, 0, Sum[If[Mod[j, 2] == 0, g[n - i*j, i-1, p + j*i]/j!/i!^j, 0], {j, 0, n/i}]]]; a[n_] := g[2*n, 2*n, 0]; Table[ a[n], {n, 0, 20}] (* Jean-François Alcover, May 12 2015, after Alois P. Heinz *)

Crossrefs

Cf. A055922, A102759, A111723, A111724.

Sequence in context: A026740 A191466 A333294 * A222687 A111874 A297944

Adjacent sequences: A130216 A130217 A130218 * A130220 A130221 A130222

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 04 2007, Aug 05 2007

Extensions

More terms from Emeric Deutsch, Sep 01 2007

Status

approved