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A089004 Number of partitions of an n-element set that have at least one odd block.

%I A089004 #8 May 04 2018 14:10:36
%S A089004 1,1,5,11,52,172,877,3761,21147,109419,678570,4063248,27644437,
%T A089004 186525861,1382958545,10323844183,82864869804,675378319788,
%U A089004 5832742205057,51386368744773,474869816156751,4486977535640087
%N A089004 Number of partitions of an n-element set that have at least one odd block.
%H A089004 Alois P. Heinz, <a href="/A089004/b089004.txt">Table of n, a(n) for n = 1..500</a>
%F A089004 E.g.f.: exp(cosh(x)-1)*(exp(sinh(x))-1).
%p A089004 with(combinat):
%p A089004 b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<1, 0,
%p A089004        add(multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1,
%p A089004        max(t, `if`(j=0, 0, irem(i, 2)))), j=0..n/i)))
%p A089004     end:
%p A089004 a:= n-> b(n$2, 0):
%p A089004 seq(a(n), n=1..30);  # _Alois P. Heinz_, Mar 08 2015
%t A089004 With[{nn=30},CoefficientList[Series[Exp[Cosh[x]-1](Exp[Sinh[x]]-1),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 04 2018 *)
%Y A089004 Cf. A000110, A005046, A003724, A086543, A087137.
%K A089004 nonn
%O A089004 1,3
%A A089004 _Vladeta Jovovic_, Nov 02 2003