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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
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
Sequence in context: A297648 A012240 A295410 * A167867 A268080 A096331
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Apr 08 2011
STATUS
approved

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Last modified June 13 03:56 EDT 2024. Contains 373366 sequences. (Running on oeis4.)