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Search: id:A161633
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| A161633 |
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E.g.f. satisfies: A(x) = 1/(1 - x*exp(x*A(x))). |
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+0
2
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| 1, 1, 4, 27, 268, 3525, 57966, 1146061, 26500552, 702069129, 20974309210, 697754762001, 25584428686620, 1025230366195789, 44579963354153878, 2090676600895922565, 105191995364927688976, 5652501986238910061073
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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E.g.f.: A(x) = 1 + x*A(x)*exp(x*A(x)).
E.g.f.: A(x) = (1/x)*Series_Reversion[x/(1 + x*exp(x))].
...
a(n) = n!*Sum_{k=0..n} C(n+1,k)/(n+1) * k^(n-k)/(n-k)!.
Let A(x)^m = Sum_{n>=0} a(n,m)*x^n/n! then
a(n,m) = n!*Sum_{k=0..n} C(n+m,k)*m/(n+m) * k^(n-k)/(n-k)!.
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 4*x^2/2! + 27*x^3/3! + 268*x^4/4! + 3525*x^5/5! +...
exp(x*A(x)) = 1 + x + 3*x^2/2! + 19*x^3/3! + 181*x^4/4! + 2321*x^5/5! +...
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PROGRAM
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(PARI) a(n, m=1)=n!*sum(k=0, n, binomial(n+m, k)*m/(n+m)*k^(n-k)/(n-k)!)
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CROSSREFS
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Cf. A161630 (e.g.f. = exp(x*A(x)). [From Paul D. Hanna (pauldhanna(AT)juno.com), Jun 23 2009]
Sequence in context: A050764 A052813 A121353 this_sequence A052871 A104653 A020558
Adjacent sequences: A161630 A161631 A161632 this_sequence A161634 A161635 A161636
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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 18 2009
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