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A052888
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E.g.f. is series reversion of log(1+x)*exp(-x)
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0
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0, 1, 3, 19, 189, 2576, 44683, 941977, 23388025, 668520163, 21622993111, 780789908240, 31135480907413, 1358965445353621, 64440211018897379, 3298807094967155971, 181322497435007616497, 10651131815012588324380
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A simple grammar.
For n>0 is true sum(a(k)*sum(((-1)^i*k^i*stirling1(n-i,k))/(i!*(n-i)!),i,0,n-k),k,1,n)=delta(n,1). [From Vladimir Kruchinin, Feb 08 2012]
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 863
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FORMULA
| E.g.f.: RootOf(_Z-exp(exp(_Z)*x)+1)
a(n) = Sum_{k=1..n} Stirling2(n, k)*n^(k-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 26 2005
a(n) = exp(-n)*Sum_{k>1} n^(k-1)*k^n/k!. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 03 2006
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MAPLE
| spec := [S, {C=Prod(Z, B), B=Set(S), S=Set(C, 1 <= card)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
| Sequence in context: A006531 A202617 A143633 * A141623 A090354 A119394
Adjacent sequences: A052885 A052886 A052887 * A052889 A052890 A052891
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KEYWORD
| easy,nonn,changed
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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