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A188679 Partial sums of binomial(3n,n)^2. 10
1, 10, 235, 7291, 252316, 9270325, 353892421, 13874930821, 554792522662, 22521121103287, 925224047453512, 38381686035811912, 1605078750713101912, 67578873844051699048, 2861782692234129345448, 121795323921169907086504 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..604

FORMULA

a(n) = sum(C(3k,k)^2, k=0..n).

Recurrence: 4*(2*n^2+7*n+6)^2 * a(n+2) -(745*n^4+4486*n^3+10093*n^2 +10056*n+3744) * a(n+1) +9*(9*n^2+27*n+20)^2 * a(n) = 0.

G.f.: (1-x)^(-1)*F(1/3,1/3,2/3,2/3;1/2,1/2,1;729*x/16), where F(a1,a2,a3,a4;b1,b2,b3;z) is a hypergeometric series.

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

MATHEMATICA

Table[Sum[Binomial[3k, k]^2, {k, 0, n}], {n, 0, 20}]

Accumulate[Table[Binomial[3n, n]^2, {n, 0, 20}]] (* Harvey P. Dale, Sep 26 2019 *)

PROG

(Maxima) makelist(sum(binomial(3*k, k)^2, k, 0, n), n, 0, 20);

CROSSREFS

Cf. A005809, A001764, A188676, A104859, A188678, A188680, A188681, A188682, A188683, A188684, A188685, A188686, A188687.

Sequence in context: A297648 A012240 A295410 * A167867 A268080 A096331

Adjacent sequences:  A188676 A188677 A188678 * A188680 A188681 A188682

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Apr 08 2011

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)