The On-Line Encyclopedia of Integer Sequences (OEIS)

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A188682

Partial sums of binomials bin(3n,n)^2/(2n+1).
(history; published version)

#14 by Harvey P. Dale at Sun Jul 10 14:31:03 EDT 2016

STATUS

editing

approved

#13 by Harvey P. Dale at Sun Jul 10 14:30:57 EDT 2016

LINKS

Harvey P. Dale, <a href="/A188682/b188682.txt">Table of n, a(n) for n = 0..606</a>

STATUS

approved

editing

#12 by Harvey P. Dale at Sun Jul 10 14:29:05 EDT 2016

STATUS

editing

approved

#11 by Harvey P. Dale at Sun Jul 10 14:29:02 EDT 2016

MATHEMATICA

Accumulate[Table[Binomial[3n, n]^2/(2n+1), {n, 0, 20}]] (* Harvey P. Dale, Jul 10 2016 *)

STATUS

approved

editing

#10 by T. D. Noe at Tue Aug 06 17:29:50 EDT 2013

STATUS

proposed

approved

#9 by Vaclav Kotesovec at Tue Aug 06 13:56:14 EDT 2013

STATUS

editing

proposed

#8 by Vaclav Kotesovec at Tue Aug 06 13:51:00 EDT 2013

FORMULA

a(n) ~ 3^(6*n+7)/(713*Pi*n^2*2^(4*n+3)). - Vaclav Kotesovec, Aug 06 2013

STATUS

approved

editing

#7 by Russ Cox at Fri Mar 30 18:55:30 EDT 2012

AUTHOR

_Emanuele Munarini (emanuele.munarini(AT)polimi.it), _, Apr 08 2011

Discussion

Fri Mar 30

18:55

OEIS Server: https://oeis.org/edit/global/279

#6 by Joerg Arndt at Thu Apr 14 12:37:28 EDT 2011

STATUS

proposed

approved

#5 by Joerg Arndt at Thu Apr 14 12:37:02 EDT 2011

NAME

Partial sums of binomials bin(3n,n)^2/(2n+1).

FORMULA

a(n) = sum(bin(3k,3*k,k)^2/(2k2*k+1),k=0..n).

Recurrence: 4*(n+2)^2*(4*n^2+16*n+15) * a(n+2) -(745*n^4+4502*n^3+10181*n^2+10216*n+3840) * a(n+1) +9*(9*n^2+27*n+20)^2 *a(n) = 0.