A344565 Triangle read by rows, for 0 <= k <= n: T(n, k) = binomial(n, k) * binomial(binomial(n + 3, 2), 2).

3, 15, 15, 45, 90, 45, 105, 315, 315, 105, 210, 840, 1260, 840, 210, 378, 1890, 3780, 3780, 1890, 378, 630, 3780, 9450, 12600, 9450, 3780, 630, 990, 6930, 20790, 34650, 34650, 20790, 6930, 990, 1485, 11880, 41580, 83160, 103950, 83160, 41580, 11880, 1485

Offset: 0

Author

Peter Luschny, May 28 2021

Keywords

• nonn
• tabl

Examples

			Triangle begins:
[0]   3;
[1]  15,     15;
[2]  45,     90,    45;
[3]  105,   315,   315,    105;
[4]  210,   840,  1260,    840,    210;
[5]  378,  1890,  3780,   3780,   1890,    378;
[6]  630,  3780,  9450,  12600,   9450,   3780,    630;
[7]  990,  6930, 20790,  34650,  34650,  20790,   6930,   990;
[8] 1485, 11880, 41580,  83160, 103950,  83160,  41580, 11880,  1485;
[9] 2145, 19305, 77220, 180180, 270270, 270270, 180180, 77220, 19305, 2145.
		

Crossrefs

Apparently a subtriangle of A344678. Row sums A344564.

Programs

Maple

T := (n, k) -> (n + 4)! / (8 * k! * (n - k)!):
for n from 0 to 9 do seq(T(n, k), k = 0..n) od;

Mathematica

T[n_, k_] := (n + 4)!/(8*k!*(n - k)!); Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, May 28 2021 *)

Formula

T(n, k) = (n + 4)! / (8 * k! * (n - k)!).