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A052813
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A simple grammar.
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2
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1, 1, 4, 27, 260, 3280, 51414, 965762, 21175496, 531317520, 15021531840, 472654558992, 16385500397496, 620612495460048, 25500923655523848, 1129909190812470840, 53705490284841870144, 2725878142900911376896
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| E.g.f. of A052807 equals log(A(x)) = -log(1-x)*A(x). - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2006
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 778
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FORMULA
| E.g.f.: -1/ln(-1/(-1+x))*LambertW(-ln(-1/(-1+x)))
a(n) = Sum_{k=0..n} |Stirling1(n, k)|*(k+1)^(k-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 12 2003
E.g.f. satisfies: A(x) = 1/(1-x)^A(x). - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2006
E.g.f.: Sum_{n>=0} (n+1)^(n-1)*(-log(1-x))^n/n!. [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 22 2009]
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EXAMPLE
| E.g.f.: A(x) = 1 + x + 4*x^2/2! + 27*x^3/3! + 260*x^4/4! +...
Log(A(x))/A(x) = -log(1-x) = x + 1/2*x^2 + 1/3*x^3 + 1/4*x^4 +...
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MAPLE
| spec := [S, {C=Cycle(Z), S=Set(B), B=Prod(C, S)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROG
| (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1/(1-x+x*O(x^n))^A); n!*polcoeff(A, n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2006
(PARI) {a(n)=n!*polcoeff(sum(m=0, n, (m+1)^(m-1)/m!*(-log(1-x+x*O(x^n)))^m), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 22 2009]
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CROSSREFS
| Cf. A052807 (log(A(x)).
Sequence in context: A177885 A050764 A177379 * A121353 A161633 A052871
Adjacent sequences: A052810 A052811 A052812 * A052814 A052815 A052816
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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