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A102287 Total number of even blocks in all partitions of n-set.

%I A102287 #14 Sep 16 2015 19:09:00
%S A102287 0,1,3,13,55,256,1274,6791,38553,232171,1477355,9898780,69621864,
%T A102287 512585529,3940556611,31560327945,262805569159,2271094695388,
%U A102287 20333574916690,188322882941471,1801737999086129,17783472151154007,180866601699482803,1893373126840572056
%N A102287 Total number of even blocks in all partitions of n-set.
%H A102287 Alois P. Heinz, <a href="/A102287/b102287.txt">Table of n, a(n) for n = 1..575</a>
%F A102287 E.g.f: (cosh(x)-1)*exp(exp(x)-1).
%e A102287 a(3)=3 because in the 5 (=A000110(3)) partitions 123, (12)/3, (13)/2, 1/(23) and 1/2/3 of {1,2,3} we have 3 blocks of even size (shown between parentheses).
%p A102287 G:=(cosh(x)-1)*exp(exp(x)-1): Gser:=series(G,x=0,28): seq(n!*coeff(Gser,x^n),n=1..25); # _Emeric Deutsch_, Jun 22 2005
%p A102287 # second Maple program:
%p A102287 with(combinat):
%p A102287 b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, 0],
%p A102287        add((p->(p+[0, `if`(i::odd, 0, j)*p[1]]))(
%p A102287        b(n-i*j, i-1))*multinomial(n, n-i*j, i$j)/j!, j=0..n/i))
%p A102287     end:
%p A102287 a:= n-> b(n$2)[2]:
%p A102287 seq(a(n), n=1..30);  # _Alois P. Heinz_, Sep 16 2015
%t A102287 Range[0, nn]! CoefficientList[
%t A102287   D[Series[Exp[y (Cosh[x] - 1) + Sinh[x]], {x, 0, nn}], y] /. y -> 1,  x]  (* _Geoffrey Critzer_, Aug 28 2012 *)
%Y A102287 Cf. A005493, A000296.
%K A102287 easy,nonn
%O A102287 1,3
%A A102287 _Vladeta Jovovic_, Feb 19 2005
%E A102287 More terms from _Emeric Deutsch_, Jun 22 2005