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A360546
Triangle read by rows: T(n, m) = (n+1-m)*C(2*n+2-m, m)*C(3*n-3*m+2, n-m+1)/(2*n-m+2).
3
1, 5, 2, 28, 20, 3, 165, 168, 50, 4, 1001, 1320, 588, 100, 5, 6188, 10010, 5940, 1568, 175, 6, 38760, 74256, 55055, 19800, 3528, 280, 7, 245157, 542640, 482664, 220220, 54450, 7056, 420, 8, 1562275, 3922512, 4069800, 2252432, 715715, 130680, 12936, 600, 9
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
Sequence in context: A117734 A007572 A297812 * A347379 A224494 A095998
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Feb 11 2023
STATUS
approved