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A096647 Number of partitions of an n-set with even number of even blocks.

%I A096647 #16 Mar 16 2015 09:40:58
%S A096647 1,1,1,2,8,27,97,443,2095,10440,58194,340375,2097933,13847485,
%T A096647 95504749,690495874,5245040408,41428115543,340899165549,2917641580783,
%U A096647 25857170687507,237421321934176,2253720620740362,22073206655954547,222987346441156585,2319379362420267753
%N A096647 Number of partitions of an n-set with even number of even blocks.
%H A096647 Alois P. Heinz, <a href="/A096647/b096647.txt">Table of n, a(n) for n = 0..500</a>
%F A096647 E.g.f.: exp(sinh(x))*cosh(cosh(x)-1).
%F A096647 a(n) = sum{k=0..n, if(mod(n-k,2)=0, A048993(n,k), 0)}. - _Paul Barry_, May 19 2006
%p A096647 with(combinat):
%p A096647 b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<1,
%p A096647       0, add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1,
%p A096647       irem(t+`if`(irem(i, 2)=0, j, 0), 2)), j=0..n/i)))
%p A096647     end:
%p A096647 a:= n-> b(n$2, 1):
%p A096647 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 08 2015
%t A096647 a[n_] := Sum[If[Mod[n-k, 2] == 0, StirlingS2[n, k], 0], {k, 0, n}]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 16 2015, after _Paul Barry_ *)
%Y A096647 Cf. A046682, A096648.
%K A096647 easy,nonn
%O A096647 0,4
%A A096647 _Vladeta Jovovic_, Aug 14 2004
%E A096647 More terms from _Emeric Deutsch_, Nov 16 2004