The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A346646 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A346646

a(n) = Sum_{k=0..n} binomial(n,k) * binomial(4*k,k) / (3*k + 1).
(history; published version)

#17 by R. J. Mathar at Thu Aug 17 05:02:11 EDT 2023

STATUS

editing

approved

#16 by R. J. Mathar at Thu Aug 17 05:01:59 EDT 2023

FORMULA

D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) -2*(2*n-1) *(91*n^2 -91*n +24)*a(n-1) +6*(n-1) *(155*n^2 -310*n +167)*a(n-2) -438*(n-1) *(n-2)*(2*n-3) *a(n-3) +283*(n-1)*(n-2) *(n-3)*a(n-4)=0. - R. J. Mathar, Aug 17 2023

STATUS

approved

editing

#15 by R. J. Mathar at Tue Jan 10 12:26:26 EST 2023

STATUS

editing

approved

#14 by R. J. Mathar at Tue Jan 10 12:26:17 EST 2023

MAPLE

A346646 := proc(n)

hypergeom([-n, 1/4, 1/2, 3/4], [2/3, 1, 4/3], -256/27) ;

simplify(%) ;

end proc:

seq(A346646(n), n=0..40) ; # R. J. Mathar, Jan 10 2023

STATUS

approved

editing

#13 by Vaclav Kotesovec at Tue Nov 16 03:07:19 EST 2021

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reviewed

approved

#12 by Michel Marcus at Tue Nov 16 00:53:55 EST 2021

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proposed

reviewed

#11 by Seiichi Manyama at Tue Nov 16 00:27:43 EST 2021

STATUS

editing

proposed

#10 by Seiichi Manyama at Tue Nov 16 00:26:10 EST 2021

LINKS

Seiichi Manyama, <a href="/A346646/b346646.txt">Table of n, a(n) for n = 0..500</a>

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approved

editing

#9 by Vaclav Kotesovec at Fri Jul 30 04:42:08 EDT 2021

STATUS

editing

approved

#8 by Vaclav Kotesovec at Fri Jul 30 04:42:05 EDT 2021

FORMULA

a(n) ~ 283^(n + 3/2) / (2048 * sqrt(2*Pi) * n^(3/2) * 3^(3*n + 3/2)). - Vaclav Kotesovec, Jul 30 2021

STATUS

approved

editing