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A188912 Binomial convolution of the binomial coefficients bin(3n,n)/(2n+1) (A001764). 3
1, 2, 8, 42, 260, 1816, 13962, 116094, 1029124, 9609144, 93569808, 942642696, 9763181946, 103455616400, 1117379189926, 12264816349938, 136501928050116, 1537591374945704, 17503603786398576, 201128739609458904, 2330480521265639136 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..93

FORMULA

a(n) = sum(binomial(n, k)*binomial(3*k, k)/(2*k+1)*binomial(3*n-3*k, n-k)/(2*n-2*k+1), k=0..n)

E.g.f: F(1/3,2/3;1,3/2;27*x/4)^2, where F(a1,a2;b1,b2;z) is a hypergeometric series.

MATHEMATICA

Table[Sum[Binomial[n, k]Binomial[3k, k]/(2k+1)Binomial[3n-3k, n-k]/(2n-2k+1), {k, 0, n}], {n, 0, 22}]

PROG

(Maxima) makelist(sum(binomial(n, k)*binomial(3*k, k)/(2*k+1)*binomial(3*n-3*k, n-k)/(2*n-2*k+1), k, 0, n), n, 0, 12);

CROSSREFS

Cf. A005809, A001764, A005809, A006256, A006013, A045721, A188911, A188913

Sequence in context: A013999 A130649 A054993 * A229285 A005315 A182520

Adjacent sequences:  A188909 A188910 A188911 * A188913 A188914 A188915

KEYWORD

nonn,easy

AUTHOR

Emanuele Munarini, Apr 13 2011

STATUS

approved

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Last modified August 17 23:07 EDT 2018. Contains 313817 sequences. (Running on oeis4.)