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%I #11 May 12 2015 09:37:57
%S 1,1,4,56,631,15457,582374,18589286,894499204,51154344582,
%T 3823359163826,274722100927166,25458967562911128,2569179797929092506,
%U 284554990016509385086,37830153187190688287522,5093072752898942262610007,798814778335473578083666573
%N Number of partitions of 2n-set in which number of blocks of size k is even (or zero) for every k.
%H Alois P. Heinz, <a href="/A130219/b130219.txt">Table of n, a(n) for n = 0..250</a>
%F E.g.f.: Product_{k>0} cosh(x^k/k!).
%e a(2)=4 because we have ab|cd, ac|bd, ad|bc and a|b|c|d.
%p 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
%p # second Maple program:
%p g:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0, add(
%p `if`(irem(j, 2)=0, g(n-i*j, i-1, p+j*i)/j!/i!^j, 0), j=0..n/i)))
%p end:
%p a:= n-> g(2*n$2, 0):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Mar 06 2015
%t 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_ *)
%Y Cf. A055922, A102759, A111723, A111724.
%K easy,nonn
%O 0,3
%A _Vladeta Jovovic_, Aug 04 2007, Aug 05 2007
%E More terms from _Emeric Deutsch_, Sep 01 2007
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