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A136507
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a(n) = Sum_{k=0..n} binomial(2^(n-k) + k, n-k).
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5
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1, 3, 10, 71, 1925, 203904, 75214965, 94608676477, 409763735870986, 6208539881584781823, 334272186911271376874561, 64832512634295914941490910360, 45811927207957062190019240099653265
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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 - 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^(n-k)+k, n-k], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Mar 08 2015 *)
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PROG
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(PARI) {a(n)=sum(k=0, n, binomial(2^(n-k)+k, n-k))}
for(n=0, 16, print1(a(n), ", "))
(PARI) /* a(n) = coefficient of x^n in o.g.f. series: */
{a(n)=polcoeff(sum(i=0, n, 1/(1-x-2^i*x^2 +x*O(x^n))*log(1+2^i*x +x*O(x^n))^i/i!), n)}
for(n=0, 16, print1(a(n), ", "))
(Sage) [sum(binomial(2^k +n-k, k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Mar 14 2021
(Magma) [(&+[Binomial(2^k +n-k, k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Mar 14 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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