OFFSET
0,5
FORMULA
T(n, k) = binomial(n, k) * A057977(n).
EXAMPLE
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;
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;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jan 09 2023
STATUS
approved