A359648 Triangle read by rows. T(n, k) = (n!)^2 / (k! * (n - k)! * (floor(n/2)!)^2 * (floor(n/2) + 1)).

1, 1, 1, 1, 2, 1, 3, 9, 9, 3, 2, 8, 12, 8, 2, 10, 50, 100, 100, 50, 10, 5, 30, 75, 100, 75, 30, 5, 35, 245, 735, 1225, 1225, 735, 245, 35, 14, 112, 392, 784, 980, 784, 392, 112, 14, 126, 1134, 4536, 10584, 15876, 15876, 10584, 4536, 1134, 126

Offset: 0

Author

Peter Luschny, Jan 09 2023

Keywords

• nonn
• tabl

Examples

			Triangle T(n, k) starts:
[0]   1;
[1]   1,    1;
[2]   1,    2,    1;
[3]   3,    9,    9,     3;
[4]   2,    8,   12,     8,     2;
[5]  10,   50,  100,   100,    50,    10;
[6]   5,   30,   75,   100,    75,    30,     5;
[7]  35,  245,  735,  1225,  1225,   735,   245,   35;
[8]  14,  112,  392,   784,   980,   784,   392,  112,   14;
[9] 126, 1134, 4536, 10584, 15876, 15876, 10584, 4536, 1134, 126;
		

Crossrefs

Cf. A057977, A063549, A240558 (row sums), A000007 (alternating row sums).

Programs

Maple

T := proc(n, k) n!^2 / (k! * (n - k)! * iquo(n,2)!^2 * (iquo(n,2) + 1)) end:
for n from 0 to 9 do seq(T(n, k), k = 0..n) od;

Formula

T(n, k) = binomial(n, k) * A057977(n).