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A052842
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E.g.f. A(x) = series reversion of (1-x)*(1-exp(-x)).
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0
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0, 1, 3, 23, 290, 5104, 115374, 3185972, 103946688, 3912527016, 166884627360, 7955159511672, 419106982360560, 24182042474691984, 1516563901865906880, 102717031449780063360, 7472238163167018081024
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A simple grammar
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 809
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FORMULA
| E.g.f. satisfies: A(x) = -log(1 - x/(1-A(x))). [From Encyclopedia of Combinatorial Structures]
a(n)=sum(k=0..n-1, (sum(j=0..k, (sum(i=0..j, (stirling2(i+n-1,j)*binomial(j,j-i))/(i+n-1)!))*(-1)^(n+j-1)/(k-j)!))*(n+k-1)!), n>0. [From Vladimir Kruchinin, Feb 06 2012]
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EXAMPLE
| E.g.f.: A(x) = x + 3*x^2/2! + 23*x^3/3! + 290*x^4/4! + 5104*x^5/5! +... which satisfies: A(x) = -log(1 - x/(1-A(x))).
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MAPLE
| spec := [S, {C=Prod(Z, B), S=Cycle(C), B=Sequence(S)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROG
| (PARI) {a(n)=n!*polcoeff(serreverse((1-exp(-x+O(x^(n+2))))*(1-x)), n)} /* Paul D. Hanna */
(Maxima) a(n):=sum((sum((sum((stirling2(i+n-1, j)*binomial(j, j-i))/(i+n-1)!, i, 0, j))*(-1)^(n+j-1)/(k-j)!, j, 0, k))*(n+k-1)!, k, 0, n-1); [From Vladimir Kruchinin, Feb 06 2012]
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CROSSREFS
| Sequence in context: A199544 A006555 A060090 * A088692 A188313 A129458
Adjacent sequences: A052839 A052840 A052841 * A052843 A052844 A052845
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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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EXTENSIONS
| Name from a comment by Paul D. Hanna, Jun 22 2011
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