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A036909 a(n) = (2/3) * 4^n * binomial(3*n, n). 0
8, 160, 3584, 84480, 2050048, 50692096, 1270087680, 32133218304, 819082035200, 21002987765760, 541167892561920, 13999778090188800, 363391162981023744, 9459706464902840320, 246865719056498950144, 6456334894356662059008 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

The right-hand side of a binomial coefficient identity in H. W. Gould, Combinatorial Identities, Morgantown, 1972; Eq. 3.116 page 35.

LINKS

Table of n, a(n) for n=1..16.

FORMULA

Sum_{k=0..n} binomial(4n, 2n-2k)*binomial(k+n, n) = (2/3)*4^n*binomial(3*n, n).

G.f.: 2*2F1(1/3,2/3;1/2;27x)/3 = 2*(cos((1/6)*arccos(1-54*x))/sqrt(1-27*x) - 1) /(3*x). - Harvey P. Dale, Mar 26 2012

MATHEMATICA

Table[2/3 4^n Binomial[3n, n], {n, 20}](* Harvey P. Dale, Mar 26 2012 *)

CROSSREFS

Sequence in context: A201030 A127369 A228700 * A221077 A052140 A219265

Adjacent sequences:  A036906 A036907 A036908 * A036910 A036911 A036912

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 21 06:40 EST 2019. Contains 320371 sequences. (Running on oeis4.)