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A096579 Number of partitions of an n-set with exactly one even block.

%I A096579 #9 May 10 2016 17:01:30
%S A096579 0,1,3,7,25,91,329,1415,6297,29431,151085,802099,4506957,26836083,
%T A096579 165586321,1074740079,7268876881,50985776815,372854157589,
%U A096579 2820244541675,22087612114805,179014336044171,1495539626297689,12894921568568999,114481871464864825
%N A096579 Number of partitions of an n-set with exactly one even block.
%H A096579 Alois P. Heinz, <a href="/A096579/b096579.txt">Table of n, a(n) for n = 1..591</a>
%F A096579 E.g.f.: exp(sinh(x))*(cosh(x)-1). More generally, e.g.f. for the number of partitions of n-set with exactly k even blocks is 1/k!*exp(sinh(x))*(cosh(x)-1)^k.
%p A096579 b:= proc(n, t) option remember; `if`(n=0, t, add(
%p A096579       `if`(t=1 and j::even, 0, binomial(n-1, j-1)*
%p A096579        b(n-j, `if`(j::even, 1, t))), j=1..n))
%p A096579     end:
%p A096579 a:= n-> b(n, 0):
%p A096579 seq(a(n), n=1..30);  # _Alois P. Heinz_, May 10 2016
%t A096579 Drop[ Range[0, 24]! CoefficientList[ Series[ E^Sinh[x]*(Cosh[x] - 1), {x, 0, 24}], x], 1] (* _Robert G. Wilson v_, Aug 17 2004 *)
%Y A096579 Cf. A003724.
%K A096579 easy,nonn
%O A096579 1,3
%A A096579 _Vladeta Jovovic_, Aug 13 2004
%E A096579 More terms from _Robert G. Wilson v_, Aug 17 2004