OFFSET
0,3
FORMULA
T(n, k) = Lah(k + n, n), where Lah denotes the unsigned Lah numbers A271703.
EXAMPLE
[0] 1;
[1] 1, 2;
[2] 1, 6, 36;
[3] 1, 12, 120, 1200;
[4] 1, 20, 300, 4200, 58800;
[5] 1, 30, 630, 11760, 211680, 3810240;
[6] 1, 42, 1176, 28224, 635040, 13970880, 307359360;
[7] 1, 56, 2016, 60480, 1663200, 43908480, 1141620480, 29682132480;
MAPLE
T := (n, k) -> ifelse(n = 0, 1, n*((k + n)!)^2 / ((k + n)*(n!)^2*k!)):
seq(seq(T(n, k), k = 0..n), n = 0..8);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jun 15 2022
STATUS
approved