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A136557
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a(n) = Sum_{k=0..n} binomial(2^k + n-k-1, k).
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3
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1, 2, 6, 45, 1436, 171836, 68149425, 89431630740, 396956313475102, 6099399658235428041, 331007760926212498510464, 64484289650612910347505873728, 45677712418497545460138258802186905
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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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Equals antidiagonal sums of square array A136555.
G.f.: A(x) = Sum_{n>=0} (1+2^n*x)^-1 * (1-x-2^n*x^2)^-1 * log(1+2^n*x)^n / n!.
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MAPLE
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MATHEMATICA
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Table[Sum[Binomial[2^k+n-k-1, 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+n-k-1, k))
(PARI) /* As coefficient of x^n in the g.f.: */ {a(n)=polcoeff(sum(i=0, n, ((1+2^i*x+x*O(x^n))*(1-x-2^i*x^2))^-1*log(1+2^i*x+x*O(x^n))^i/i!), n)}
(Sage) [sum(binomial(2^k +n-k-1, k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Mar 15 2021
(Magma) [(&+[Binomial(2^k +n-k-1, k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Mar 15 2021
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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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