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Search: id:A136648
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| A136648 |
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Inverse binomial transform of A014070: a(n) = Sum_{k=0..n} (-1)^(n-k)*C(n,k)*C(2^k,k). |
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+0
1
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| 1, 1, 3, 43, 1625, 192785, 73792371, 94005141667, 408909577044065, 6204433373664395569, 334203804752658372354515, 64828498485572980097719939179, 45811084061472137471487315433296153
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: A(x) = (1/(1+x))*Sum_{n>=0} [log(1 + (2^n+1)*x) - log(1+x)]^n / n!.
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MAPLE
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(PARI) {a(n)=sum(k=0, n, (-1)^(n-k)*binomial(n, k)*binomial(2^k, k))} (PARI) /* Using the g.f.: */ {a(n)=local(X=x+x*O(x^n)); polcoeff(sum(k=0, n, (log(1+(2^k+1)*X)-log(1+X))^k/k!)/(1+X), n)}
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CROSSREFS
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Cf. A014070 (C(2^n, n)), A134174.
Adjacent sequences: A136645 A136646 A136647 this_sequence A136649 A136650 A136651
Sequence in context: A099664 A093163 A141060 this_sequence A114337 A009720 A076361
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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) and Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 21 2008
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