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Search: id:A088692
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| A088692 |
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E.g.f: A(x) = f(x*A(x)), where f(x)=(1+2*x)*exp(x). |
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+0
3
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| 1, 3, 23, 304, 5829, 147696, 4670371, 177383424, 7874174601, 400298556160, 22940919680271, 1463679309053952, 102911522568495757, 7906731860604186624, 659108356837269579675, 59252790438687592677376
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OFFSET
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0,2
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COMMENT
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Radius of convergence of A(x): r = (1/4)*exp(-1/2) = 0.151632.., where A(r) = 2*exp(1/2), and r = limit a(n)/a(n+1)*n as n->infinity.
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FORMULA
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a(n) equals the coefficient of x^n in ((1+2*x)*exp(x))^(n+1)/(n+1).
a(n) = Sum_{k=1..n} 2^(n-k)*n^(k-2)*n!/k!*binomial(n-1,k-1) (offset 1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jun 19 2006
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PROGRAM
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(PARI) a(n)=n!*polcoeff(((1+2*x)*exp(x))^(n+1)+x*O(x^n), n, x)/(n+1)
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CROSSREFS
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Cf. A088690, A088693.
Sequence in context: A006555 A060090 A052842 this_sequence A129458 A118184 A027486
Adjacent sequences: A088689 A088690 A088691 this_sequence A088693 A088694 A088695
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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), Oct 07 2003
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