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A356636
Triangle read by rows. T(n, k) = binomial(n, k) * n!^2 / floor(n/2)!^2.
1
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
0,4
FORMULA
T(n, 0) = T(n, n) = A193282(n).
Sum_{k=0..n} T(n, k) = 2^n * A193282(n).
EXAMPLE
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;
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;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Aug 19 2022
STATUS
approved