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#29 by N. J. A. Sloane at Thu Jan 30 21:29:15 EST 2020
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D-finite with recurrence: (n+2)*a(n) - (2*n+1)*a(n-1) + 23*(1-n)*a(n-2) = 0. - R. J. Mathar, Sep 26 2012
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Discussion
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| Thu Jan 30
| 21:29
| OEIS Server: https://oeis.org/edit/global/2847
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#28 by R. J. Mathar at Wed Jan 22 15:04:22 EST 2020
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#27 by R. J. Mathar at Wed Jan 22 15:04:16 EST 2020
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ConjectureD-finite: (n+2)*a(n) - (2*n+1)*a(n-1) + 23*(1-n)*a(n-2) = 0. - R. J. Mathar, Sep 26 2012
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approved
editing
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#26 by Bruno Berselli at Fri May 26 08:35:24 EDT 2017
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#25 by Bruno Berselli at Fri May 26 08:35:20 EDT 2017
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#24 by Bruno Berselli at Fri May 26 08:34:00 EDT 2017
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Expansion of (1- - x- - sqrt(1-2x-23x - 2*x - 23*x^2))/(12x12*x^2).
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G.f.: 2/(1- - x+ + sqrt(1-2x-23x - 2*x - 23*x^2)).
a(n) = sum{Sum_{k=0..n, } binomial(n, k))*6^(k/2))*C(k/2)()*(1+(- + (-1)^k)/2}, with C(n)=A000108(n).
a(n) = sum{Sum_{k=0..n, } C(n, 2k)2*k)*C(k))*6^k}; - _. - _Paul Barry_, May 16 2005
Conjecture: (n+2)*a(n) -() - (2*n+1)*a(n-1) +) + 23*(1-n)*a(n-2)=) = 0. - R. J. Mathar, Sep 26 2012
a(n) ~ sqrt(9/4+ + 73/(24*sqrt(6)))/(n^(3/2)*sqrt(Pi))*(1+ + 2*sqrt(6))^n. - Vaclav Kotesovec, Sep 29 2012
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approved
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#23 by Bruno Berselli at Fri May 26 08:22:09 EDT 2017
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#22 by Joerg Arndt at Fri May 26 08:10:33 EDT 2017
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#21 by Ilya Gutkovskiy at Fri May 26 07:38:09 EDT 2017
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#20 by Ilya Gutkovskiy at Fri May 26 07:35:46 EDT 2017
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