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Search: id:A161605
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| A161605 |
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E.g.f. satisfies: A(x) = exp(x*exp(x*A(x)^3)). |
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+0
1
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| 1, 1, 3, 28, 365, 6496, 147127, 4033408, 130058777, 4822981120, 202225551371, 9460961327104, 488602134968389, 27609977350868992, 1694576741234926655, 112258296102497099776, 7983577042683934226993, 606688287932557859356672
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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More generally, if G(x) = exp(x*exp(x*G(x)^p)),
where G(x)^m = Sum_{n>=0} g(n,m)*x^n/n!,
then g(n,m) = Sum_{k=0..n} C(n,k) * m*(p*(n-k) + m)^(k-1) * k^(n-k).
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FORMULA
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a(n) = Sum_{k=0..n} C(n,k) * (3*(n-k) + 1)^(k-1) * k^(n-k).
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 365*x^4/4! +...
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, binomial(n, k)*(3*(n-k)+1)^(k-1)*k^(n-k))}
(PARI) {a(n)=local(A=1+x); for(i=0, n, A=exp(x*exp(x*A^3+O(x^n)))); n!*polcoeff(A, n, x)}
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CROSSREFS
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Cf. A161552, A161567.
Adjacent sequences: A161602 A161603 A161604 this_sequence A161606 A161607 A161608
Sequence in context: A026114 A072343 A151423 this_sequence A048954 A086569 A143636
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 14 2009
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