A356636 Triangle read by rows. T(n, k) = binomial(n, k) * n!^2 / floor(n/2)!^2.

1, 1, 1, 4, 8, 4, 36, 108, 108, 36, 144, 576, 864, 576, 144, 3600, 18000, 36000, 36000, 18000, 3600, 14400, 86400, 216000, 288000, 216000, 86400, 14400, 705600, 4939200, 14817600, 24696000, 24696000, 14817600, 4939200, 705600

Offset: 0

Author

Peter Luschny, Aug 19 2022

Keywords

• nonn
• tabl

Examples

			Triangle T(n, k) starts:
[0]     1;
[1]     1,     1;
[2]     4,     8,      4;
[3]    36,   108,    108,     36;
[4]   144,   576,    864,    576,    144;
[5]  3600, 18000,  36000,  36000,  18000,  3600;
[6] 14400, 86400, 216000, 288000, 216000, 86400, 14400;
		

Crossrefs

Cf. A056040, A193282, A253666.

Programs

Maple

A356636 := (n, k) -> binomial(n, k) * (n! / iquo(n, 2)!) ^ 2:
for n from 0 to 9 do seq(A356636(n, k), k = 0..n) od;

Formula

T(n, 0) = T(n, n) = A193282(n).

Sum_{k=0..n} T(n, k) = 2^n * A193282(n).