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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
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1, 4, 16, 136, 3900, 410704, 150779216, 189354108224, 819706419291728, 12417873698752685696, 668556572391910046409088, 129665687275486846550512590336, 91623983383737723477835280780455168, 238057598315149125515904595621291745671168, 2291332225550784443587332334013451028612830795776
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OFFSET
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0,2
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LINKS
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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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MATHEMATICA
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Table[Sum[Binomial[2^k, k]*Binomial[2^(n-k), n-k], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
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PROG
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(PARI) {a(n) = sum(k=0, n, binomial(2^k, k) * binomial(2^(n-k), n-k) )}
for(n=0, 20, print1(a(n), ", "))
(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)}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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