A360560 - OEIS

A360560

Triangle read by rows. T(n, k) = (1/2) * C(n, k) * C(3*n - 1, n) for n > 0 and T(0, 0) = 1.

1, 1, 1, 5, 10, 5, 28, 84, 84, 28, 165, 660, 990, 660, 165, 1001, 5005, 10010, 10010, 5005, 1001, 6188, 37128, 92820, 123760, 92820, 37128, 6188, 38760, 271320, 813960, 1356600, 1356600, 813960, 271320, 38760, 245157, 1961256, 6864396, 13728792, 17160990, 13728792, 6864396, 1961256, 245157

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..44.

FORMULA

G.f.: 1/2 + x*sqrt(3 + 3*y)*cot(arcsin((3*sqrt(3*x*(y + 1)))/2)/3)/ (2*sqrt(4*x - 27*x^2*(y + 1))).

EXAMPLE

Triangle begins:

1, 1;

5, 10, 5;

28, 84, 84, 28;