The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A167867 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A167867

a(n) = 2^n * Sum_{k=0..n} binomial(2*k,k)^3 / 2^k.
(history; published version)

#14 by Peter Luschny at Mon Jun 07 01:10:48 EDT 2021

STATUS

reviewed

approved

#13 by Hugo Pfoertner at Sun Jun 06 16:35:15 EDT 2021

STATUS

proposed

reviewed

#12 by Jon E. Schoenfield at Sun Jun 06 12:12:39 EDT 2021

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Sun Jun 06 12:12:37 EDT 2021

NAME

a(n) = 2^n * Sum_{ k=0..n } binomial(2*k,k)^3 / 2^k.

FORMULA

a(n) = 2^n * Sum[ Binomial[_{k=0..n} binomial(2*k,k])^3 / 2^k, {k,0,n} ].

STATUS

approved

editing

#10 by Charles R Greathouse IV at Sun Aug 03 14:26:33 EDT 2014

MATHEMATICA

Table[2^n Sum[Binomial[2k, k]^3/2^k, {k, 0, n}], {n, 0, 30}] (* _Vincenzo Librandi, _, Mar 26 2012 *)

Discussion

Sun Aug 03

14:26

OEIS Server: https://oeis.org/edit/global/2270

#9 by Joerg Arndt at Tue Aug 13 06:24:01 EDT 2013

STATUS

proposed

approved

#8 by Vaclav Kotesovec at Tue Aug 13 05:53:43 EDT 2013

STATUS

editing

proposed

#7 by Vaclav Kotesovec at Tue Aug 13 05:53:33 EDT 2013

FORMULA

Recurrence: n^3*a(n) = 2*(33*n^3 - 48*n^2 + 24*n - 4)*a(n-1) - 16*(2*n-1)^3*a(n-2). - Vaclav Kotesovec, Aug 13 2013

a(n) ~ 2^(6*n+5)/(31*(Pi*n)^(3/2)). - Vaclav Kotesovec, Aug 13 2013

STATUS

approved

editing

#6 by Russ Cox at Sat Mar 31 13:20:40 EDT 2012

AUTHOR

_Alexander Adamchuk (alex(AT)kolmogorov.com), _, Nov 14 2009

Discussion

Sat Mar 31

13:20

OEIS Server: https://oeis.org/edit/global/879

#5 by Russ Cox at Fri Mar 30 18:39:37 EDT 2012

EXTENSIONS

More terms from _Sean A. Irvine (sairvin(AT)xtra.co.nz), _, Apr 27 2010

Discussion

Fri Mar 30

18:39

OEIS Server: https://oeis.org/edit/global/220