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A053488
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E.g.f.: exp(exp(sinh(x))-1)-1.
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0
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0, 1, 2, 6, 23, 103, 535, 3153, 20676, 149148, 1172343, 9960085, 90864801, 885278605, 9167936406, 100508961982, 1162366436355, 14136151459043, 180287711599455, 2405321659729837, 33495442060505752, 485880832780748932
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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.
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REFERENCES
| R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.1.14.
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LINKS
| Vladimir Kruchinin, Compositae and their properties, arXiv:1103.2582~
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FORMULA
| a(n)=sum(m=1..n, sum(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. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 10 2010]
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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*)
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PROG
| (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); [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 10 2010]
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CROSSREFS
| Sequence in context: A022558 A005802 A061552 * A117106 A137534 A137535
Adjacent sequences: A053485 A053486 A053487 * A053489 A053490 A053491
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 15 2000
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