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Search: id:A136649
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| A136649 |
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Binomial transform of A014070: a(n) = Sum_{k=0..n} C(n,k)*C(2^k,k). |
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+0
1
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| 1, 3, 11, 81, 2089, 211107, 76211147, 95054910473, 410422012327681, 6211807332775516467, 334327967114349983723899, 64835852334793138873642165105, 45812640033676518721399820389451657
(list; graph; listen)
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OFFSET
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0,2
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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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PROGRAM
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(PARI) {a(n)=sum(k=0, n, 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)), A134173.
Sequence in context: A163856 A099341 A129114 this_sequence A062580 A097495 A157980
Adjacent sequences: A136646 A136647 A136648 this_sequence A136650 A136651 A136652
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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.rs), Jan 21 2008
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EXTENSIONS
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Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
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