The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A346665

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A346665

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(5*k,k) / (4*k + 1).
(history; published version)

#17 by R. J. Mathar at Thu Aug 17 04:45:54 EDT 2023

STATUS

editing

approved

#16 by R. J. Mathar at Thu Aug 17 04:45:45 EDT 2023

MAPLE

A346665 := proc(n)

add((-1)^(n-k)*binomial(n, k)*binomial(5*k, k)/(4*k+1), k=0..n) ;

end proc:

seq(A346665(n), n=0..80); # R. J. Mathar, Aug 17 2023

#15 by R. J. Mathar at Thu Aug 17 04:44:59 EDT 2023

FORMULA

D-finite with recurrence 8*n*(4*n+1)*(2*n-1)*(4*n-1)*a(n) -(n-1) *(1845*n^3 -1333*n^2 -238*n +240)*a(n-1) -4*(n-1) *(2485*n^3 -7263*n^2 +7388*n -2580) *a(n-2) -2*(n-1) *(n-2) *(8095*n^2 -24029*n +18924) *a(n-3) -4*(n-1) *(n-2) *(n-3) *(2805*n -5578) *a(n-4) -2869*(n-1) *(n-2) *(n-3) *(n-4) *a(n-5)=0. - R. J. Mathar, Aug 17 2023

STATUS

approved

editing

#14 by Vaclav Kotesovec at Sat Nov 20 07:18:57 EST 2021

STATUS

proposed

approved

#13 by Seiichi Manyama at Sat Nov 20 06:50:00 EST 2021

STATUS

editing

proposed

#12 by Seiichi Manyama at Sat Nov 20 06:10:48 EST 2021

LINKS

Seiichi Manyama, <a href="/A346665/b346665.txt">Table of n, a(n) for n = 0..958</a>

STATUS

approved

editing

#11 by Vaclav Kotesovec at Fri Jul 30 04:28:54 EDT 2021

STATUS

editing

approved

#10 by Vaclav Kotesovec at Fri Jul 30 04:28:46 EDT 2021

FORMULA

a(n) ~ 2869^(n + 3/2) / (78125 * sqrt(Pi) * n^(3/2) * 2^(8*n + 7/2)). - Vaclav Kotesovec, Jul 30 2021

STATUS

approved

editing

#9 by Bruno Berselli at Wed Jul 28 04:13:20 EDT 2021

STATUS

reviewed

approved

#8 by Hugo Pfoertner at Wed Jul 28 04:03:39 EDT 2021

STATUS

proposed

reviewed