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A132684
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a(n) = binomial(2^n + n + 1, n).
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13
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1, 4, 21, 220, 5985, 501942, 143218999, 145944307080, 542150225230185, 7398714129087308170, 372134605932348010322571, 69146263065062394421802892300, 47589861944854471977019273909187085
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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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a(n) = [x^n] 1/(1-x)^(2^n + 2).
G.f.: Sum_{n>=0} (-log(1 - 2^n*x))^n / ((1 - 2^n*x)^2*n!). - Paul D. Hanna, Feb 25 2009
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EXAMPLE
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G.f.: A(x) = 1 + 4*x + 21*x^2 + 220*x^3 + 5985*x^4 + 501942*x^5 +...
A(x) = 1/(1-x)^2 - log(1-2x)/(1-2x)^2 + log(1-4x)^2/((1-4x)^2*2!) - log(1-8x)^3/((1-8x)^2*3!) +- ... (End)
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MAPLE
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MATHEMATICA
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Table[Binomial[2^n+n+1, n], {n, 0, 20}] (* Harvey P. Dale, Nov 10 2011 *)
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PROG
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(PARI) a(n)=binomial(2^n+n+1, n)
(PARI) {a(n)=polcoeff(sum(m=0, n, (-log(1-2^m*x))^m/((1-2^m*x +x*O(x^n))^2*m!)), n)} \\ Paul D. Hanna, Feb 25 2009
(Sage) [binomial(2^n +n+1, n) for n in (0..20)] # G. C. Greubel, Mar 14 2021
(Magma) [Binomial(2^n +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), A136505 (0,1), A136506 (0,2), A060690 (1,-1), A132683 (1,0), this sequence (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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