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).

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

Links

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

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

Cf. A025174, A134481.

Sequence in context: A117734 A007572 A297812 * A347379 A224494 A095998

Adjacent sequences: A360543 A360544 A360545 * A360547 A360548 A360549

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Feb 11 2023

Status

approved