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A052807
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A simple grammar.
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3
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0, 1, 3, 17, 146, 1704, 25284, 456224, 9702776, 237711888, 6593032560, 204212077992, 6986942528400, 261700394006232, 10650713784774504, 468007296229553880, 22083086552247101184, 1113646609708909274880
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OFFSET
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0,3
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COMMENTS
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E.g.f. of A052813 equals exp(A(x)) = -A(x)/log(1-x). a(n) = n!*Sum_{k=0..n-1} A052813(k)/k!/(n-k). - Paul D. Hanna, Jul 19 2006
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LINKS
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Table of n, a(n) for n=0..17.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 769
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FORMULA
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E.g.f.: -LambertW(-ln(-1/(-1+x)))
a(n) = Sum_{k=1..n} |Stirling1(n, k)|*k^(k-1). - Vladeta Jovovic, Sep 17 2003
E.g.f. satisfies: A(x) = 1/(1-x)^A(x). - Paul D. Hanna, Jul 19 2006
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EXAMPLE
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E.g.f.: A(x) = x + 3*x^2/2! + 17*x^3/3! + 146*x^4/4! +...
A(x)/exp(A(x)) = -log(1-x) = x + 1/2*x^2 + 1/3*x^3 + 1/4*x^4 +...
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MAPLE
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spec := [S, {B=Cycle(Z), C=Set(S), S=Prod(C, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1/(1-x+x*O(x^n))^A); n!*polcoeff(log(A), n)} - Paul D. Hanna, Jul 19 2006
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CROSSREFS
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Cf. A052813 (exp(A(x)).
Sequence in context: A015735 A140983 A138013 * A080253 A009813 A213507
Adjacent sequences: A052804 A052805 A052806 * A052808 A052809 A052810
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KEYWORD
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easy,nonn,changed
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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