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%I #26 Jan 19 2017 02:33:53
%S 0,1,2,6,23,103,535,3153,20676,149148,1172343,9960085,90864801,
%T 885278605,9167936406,100508961982,1162366436355,14136151459043,
%U 180287711599455,2405321659729837,33495442060505752,485880832780748932
%N E.g.f.: exp(exp(sinh(x))-1)-1.
%C a(n) is the number of pairs (d,d') of set partitions of {1,2,...,n} such that d is finer than d' and all block sizes of d are odd. - _Geoffrey Critzer_, Dec 28 2011
%D R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.1.14.
%H G. C. Greubel, <a href="/A053488/b053488.txt">Table of n, a(n) for n = 0..400</a>
%H Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011.
%F a(n) = Sum_{m=1..n} ( Sum_{k} 1/(2^k*k!)*Sum_{i=0..k} (-1)^i*binomial(k,i)*(k-2*i)^n)*stirling2(k,m),k,m,n)), n>0. - _Vladimir Kruchinin_, Sep 10 2010
%t nn = 21; a = Sinh[x]; Range[0, nn]! CoefficientList[Series[Exp[Exp[a] - 1] - 1, {x, 0, nn}], x] (* _Geoffrey Critzer_, Dec 28 2011 *)
%o (Maxima) a(n):=sum(sum(1/(2^k*k!)*sum((-1)^i*binomial(k,i)*(k-2*i)^n,i,0,k)*stirling2(k,m),k,m,n),m,1,n); /* _Vladimir Kruchinin_, Sep 10 2010 */
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jan 15 2000
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