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Search: id:A136651
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| A136651 |
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Self-convolution of A014070: a(n) = Sum_{k=0..n} C(2^k,k)*C(2^(n-k),n-k). |
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+0
1
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| 1, 4, 16, 136, 3900, 410704, 150779216, 189354108224, 819706419291728, 12417873698752685696, 668556572391910046409088, 129665687275486846550512590336, 91623983383737723477835280780455168
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OFFSET
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0,2
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FORMULA
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G.f.: A(x) = Sum_{n>=0} (1/n!)Sum_{k=0..n} C(n,k)*log(1+2^k*x)^k*log(1+2^(n-k)*x)^(n-k).
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, binomial(2^k, k)*binomial(2^(n-k), n-k))} (PARI) {a(n)=polcoeff(sum(m=0, n, sum(k=0, m, log(1+2^k*x +x*O(x^n))^k/k!*log(1+2^(m-k)*x +x*O(x^n))^(m-k)/(m-k)!)), n)}
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CROSSREFS
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Cf. A014070 (C(2^n, n)).
Sequence in context: A094356 A061129 A061131 this_sequence A005749 A005739 A005741
Adjacent sequences: A136648 A136649 A136650 this_sequence A136652 A136653 A136654
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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), Jan 16 2008
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