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Number of partitions of an n-set with even number of even blocks.
2

%I #16 Mar 16 2015 09:40:58

%S 1,1,1,2,8,27,97,443,2095,10440,58194,340375,2097933,13847485,

%T 95504749,690495874,5245040408,41428115543,340899165549,2917641580783,

%U 25857170687507,237421321934176,2253720620740362,22073206655954547,222987346441156585,2319379362420267753

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

%H Alois P. Heinz, <a href="/A096647/b096647.txt">Table of n, a(n) for n = 0..500</a>

%F E.g.f.: exp(sinh(x))*cosh(cosh(x)-1).

%F a(n) = sum{k=0..n, if(mod(n-k,2)=0, A048993(n,k), 0)}. - _Paul Barry_, May 19 2006

%p with(combinat):

%p b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<1,

%p 0, add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1,

%p irem(t+`if`(irem(i, 2)=0, j, 0), 2)), j=0..n/i)))

%p end:

%p a:= n-> b(n$2, 1):

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Mar 08 2015

%t 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 Cf. A046682, A096648.

%K easy,nonn

%O 0,4

%A _Vladeta Jovovic_, Aug 14 2004

%E More terms from _Emeric Deutsch_, Nov 16 2004