Revision History for A132684
(Underlined text is an addition;
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Showing entries 1-10
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#17 by Susanna Cuyler at Sun Mar 14 18:44:25 EDT 2021
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#16 by G. C. Greubel at Sun Mar 14 16:57:20 EDT 2021
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#15 by G. C. Greubel at Sun Mar 14 16:56:44 EDT 2021
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| LINKS
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G. C. Greubel, <a href="/A132684/b132684.txt">Table of n, a(n) for n = 0..50</a>
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| MAPLE
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A132684:= n-> binomial(2^n +n+1, n); seq(A132684(n), n=0..20); # G. C. Greubel, Mar 14 2021
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| PROG
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(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).
Cf. A060690, A132683A136555.
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approved
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#14 by Alois P. Heinz at Sat Mar 03 23:05:39 EST 2018
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#13 by Alois P. Heinz at Sat Mar 03 23:05:36 EST 2018
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| EXAMPLE
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Contribution fromFrom Paul D. Hanna, Feb 25 2009: (Start)
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approved
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#12 by Alois P. Heinz at Sat Mar 03 23:05:10 EST 2018
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#11 by Jon E. Schoenfield at Sat Mar 03 23:00:46 EST 2018
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#10 by Jon E. Schoenfield at Sat Mar 03 23:00:39 EST 2018
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| NAME
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a(n) = Cbinomial(2^n + n + 1, n).
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| EXAMPLE
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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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| PROG
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(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)} [From _)} \\ _Paul D. Hanna_, Feb 25 2009]
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| CROSSREFS
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Cf. A066384. [From _. - _Paul D. Hanna_, Feb 25 2009]
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| STATUS
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approved
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#9 by Vaclav Kotesovec at Sat Jul 02 09:56:22 EDT 2016
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#8 by Vaclav Kotesovec at Sat Jul 02 09:56:11 EDT 2016
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| FORMULA
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G.f.: Sum_{n>=0} (-log(1 - 2^n*x))^n / ((1 - 2^n*x)^2*n!). [From _!). - _Paul D. Hanna_, Feb 25 2009]
a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016
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approved
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