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A138764
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E.g.f. A(x) equals the inverse function of log(x)/(x + x^2).
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2
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1, 2, 16, 248, 5824, 184512, 7379200, 356956672, 20274442240, 1322971320320, 97542692798464, 8020249539919872, 727662513046159360, 72215332738579824640, 7782298855258810482688, 905031449967822916026368
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| E.g.f. satisfies: A(x) = exp( x*[A(x) + A(x)^2] ).
a(n) = Sum_{k=0..n} binomial(n,k)*(n+k+1)^(n-1) - due to Vladeta Jovovic (vladeta(AT)eunet.yu), Mar 31 2008.
a(n) = A138860(n)*2^n.
E.g.f. satisfies: A( x/( exp(x) + exp(2*x) ) ) = exp(x).
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EXAMPLE
| E.g.f. A(x) = 1 + 2x + 16x^2/2! + 248x^3/3! + 5824x^4/4! +...
Let r = radius of convergence of A(x), then:
r = 0.116689393840305520533609707610483991781804638898970699779...
A(r) = 1.835037067429188745641951736620284283425600418229813004773...
where A(r) and r satisfy:
A(r) = exp( (1 + A(r))/(1 + 2*A(r)) ) and r = 1/[A(r)*(1 + 2*A(r))].
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PROG
| (PARI) {a(n)=local(A=1+x); for(i=0, n, A=exp(x*(A+A^2 +x*O(x^n)))); n!*polcoeff(A, n)}
(PARI) /* Formula due to Vladeta Jovovic: */ {a(n)=sum(k=0, n, binomial(n, k)*(n+k+1)^(n-1))}
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CROSSREFS
| Cf. A138860.
Sequence in context: A188560 A012462 A012457 * A009833 A009044 A019318
Adjacent sequences: A138761 A138762 A138763 * A138765 A138766 A138767
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Mar 29 2008
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