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A136505
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a(n) = binomial(2^n + 1, n).
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14
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1, 3, 10, 84, 2380, 237336, 82598880, 99949406400, 422825581068000, 6318976181520699840, 337559127276933693852160, 65182103393445184131620004864, 45946437874792132748338425828443136
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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 + 2^n*x) * log(1 + 2^n*x)^n/n!.
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MAPLE
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MATHEMATICA
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PROG
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(PARI) {a(n)=polcoeff(sum(i=0, n, (1+2^i*x +x*O(x^n))*log(1+2^i*x +x*O(x^n))^i/i!), n)}
(Sage) [binomial(2^n +1, n) for n in (0..20)] # G. C. Greubel, Mar 14 2021
(Magma) [Binomial(2^n +1, n): n in [0..20]]; // G. C. Greubel, Mar 14 2021
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CROSSREFS
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Sequences of the form binomial(2^n +p*n +q, n): A136556 (0,-1), A014070 (0,0), this sequence (0,1), A136506 (0,2), A060690 (1,-1), A132683 (1,0), A132684 (1,1), A132685 (2,0), A132686 (2,1), A132687 (3,-1), A132688 (3,0), A132689 (3,1).
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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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