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A278884
a(n) = binomial(3*n-1,n) * binomial(3*n,n)/(2*n+1).
3
1, 2, 30, 672, 18150, 546546, 17672928, 600935040, 21212454582, 770748371250, 28657235757150, 1085694550387200, 41778588391394400, 1628982594897249312, 64234570537702934400, 2557710564063135005184, 102714012593435476016982, 4155894894567674772785250, 169274181059121504574121550, 6935873114065443534326340000, 285716428631735196825345889350, 11826871503027977442890882704050, 491714173272153004121882711232000
OFFSET
0,2
COMMENTS
Central terms of triangles A278881 and A278882; a(n) = A278881(2*n,n) for n>=0.
LINKS
FORMULA
4*n^2*(2*n-1)*(2*n+1)*a(n) -9*(3*n-1)^2*(3*n-2)^2*a(n-1)=0. - R. J. Mathar, Dec 02 2016
MATHEMATICA
Table[(Binomial[3n-1, n]Binomial[3n, n])/(2n+1), {n, 0, 50}] (* Harvey P. Dale, Mar 26 2023 *)
PROG
(PARI) {a(n) = binomial(3*n-1, n) * binomial(3*n, n) / (2*n+1)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A282733 A363113 A160694 * A013525 A270531 A229781
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 29 2016
STATUS
approved