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A167868 a(n) = 3^n*Sum_{ k=0..n } binomial(2*k,k)^3/3^k 5
1, 11, 249, 8747, 369241, 17110731, 840221217, 42944901219, 2260581606657, 121714776747971, 6671749658197129, 371062413164972955, 20887218937200347281, 1187720356043817041843, 68124474120573747125529 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The expression a(n) = B^n*Sum_{ k=0..n } binomial(2*k,k)/B^k gives A006134 for B=1, A082590 (B=2), A132310 (B=3), A002457 (B=4), A144635 (B=5), A167713 (B=16).

The expression a(n) = B^n*Sum_{ k=0..n } binomial(2*k,k)^3/B^k gives A079727 for B=1, A167867 (B=2), A167868 (B=3), A167869 (B=4), A167870 (B=16), A167871 (B=64).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

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

Recurrence: n^3*a(n) = (67*n^3 - 96*n^2 + 48*n - 8)*a(n-1) - 24*(2*n-1)^3*a(n-2). - Vaclav Kotesovec, Aug 13 2013

a(n) ~ 2^(6*n+6)/(61*(Pi*n)^(3/2)). - Vaclav Kotesovec, Aug 13 2013

MATHEMATICA

Table[3^n Sum[Binomial[2k, k]^3/3^k, {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Mar 26 2012 *)

CROSSREFS

Cf. A079727, A167867, A167868, A167869, A167870, A167872.

Cf. A000984, A066796, A006134, A082590, A132310, A002457, A144635, A167713, A167859.

Sequence in context: A219089 A243683 A323255 * A238751 A098672 A056210

Adjacent sequences:  A167865 A167866 A167867 * A167869 A167870 A167871

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Nov 14 2009

EXTENSIONS

More terms from Sean A. Irvine, Apr 27 2010

STATUS

approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)