OFFSET
0,2
FORMULA
G.f.: -1/(2*x) + (sqrt(3)*cot((1/3)*arcsin((3*sqrt(3)*sqrt(x))/(2- 2*x*y))))/ (2*sqrt(x*(-27*x + 4*(-1+x*y)^2))).
EXAMPLE
Triangle begins:
1;
5, 2;
28, 20, 3;
165, 168, 50, 4;
1001, 1320, 588, 100, 5;
6188, 10010, 5940, 1568, 175, 6;
MAPLE
A360546 := proc(n, k) m := n-k+1; (1/3)*binomial(3*m, m)*binomial(m + n, k) end:
seq(print(seq(A360546(n, k), k = 0..n)), n = 0..8); # Peter Luschny, Feb 11 2023
PROG
(Maxima)
T(n, m):=if n<m then 0 else ((n+1-m)*binomial(2*n+2-m, m)*binomial(3*n-3*m+2, n-m+1))/(2*n-m+2);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Feb 11 2023
STATUS
approved