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A052892
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E.g.f. is series reversion of log(1+x)*(1-x)
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0
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0, 1, 3, 22, 269, 4606, 101407, 2728818, 86783769, 3184595686, 132443395091, 6156200036746, 316272966462565, 17795937622944846, 1088410048965734055, 71893314170319604066, 5100574859506418167601, 386824334429004242804086
(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(k=1..n, a(k)*sum(j=k..n, (binomial(k,n-j)*(-1)^(n-j)*stirling1(j,k))/j!))=delta(n,1). [From Vladimir Kruchinin, Feb 08 2012]
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 868
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FORMULA
| E.g.f.: exp(RootOf(-2*_Z+_Z*exp(x*_Z)+1)*x)-1
G.f.: x*Sum_{k>0} 1/(2-k*x)^k. - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 23 2006
a(n)=((-1)^(n-1)*(n-1)!*sum(k=0..n-1, (sum(j=0..k, j!*(sum(i=j..n+j-1, (stirling1(i,j)*(-1)^(i)*binomial(j,n+j-i-1))/i!))*binomial(k,j))) *binomial(n+k-1,n-1))), n>0. [From Vladimir Kruchinin, Feb 08 2012]
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MAPLE
| spec := [S, {C=Prod(Z, B), S=Set(C, 1 <= card), B=Sequence(S)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROG
| (Maxima) a(n):=((-1)^(n-1)*(n-1)!*sum((sum(j!*(sum((stirling1(i, j)*(-1)^(i)*binomial(j, n+j-i-1))/i!, i, j, n+j-1))*binomial(k, j), j, 0, k))*binomial(n+k-1, n-1), k, 0, n-1)); [From Vladimir Kruchinin, Feb 06 2012]
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CROSSREFS
| Sequence in context: A054594 A005264 A195512 * A155806 A196022 A074706
Adjacent sequences: A052889 A052890 A052891 * A052893 A052894 A052895
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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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