A053488 E.g.f.: exp(exp(sinh(x))-1)-1.

0, 1, 2, 6, 23, 103, 535, 3153, 20676, 149148, 1172343, 9960085, 90864801, 885278605, 9167936406, 100508961982, 1162366436355, 14136151459043, 180287711599455, 2405321659729837, 33495442060505752, 485880832780748932, 7328433495203878939, 114737387813829452625

Offset: 0

Author

N. J. A. Sloane, Jan 15 2000

Keywords

• nonn

Comments

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

References

• R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.1.14.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..400
• Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011.

Programs

Mathematica

nn = 21; a = Sinh[x]; Range[0, nn]! CoefficientList[Series[Exp[Exp[a] - 1] - 1, {x, 0, nn}], x]  (* Geoffrey Critzer, Dec 28 2011 *)

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 */

Formula

a(n) = Sum_{m=1..n} Sum_{k=m..n} (Stirling2(k,m)/(2^k*k!))*Sum_{i=0..k} (-1)^i*binomial(k,i)*(k-2*i)^n. - Vladimir Kruchinin, Sep 10 2010