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A355005
Table read by rows. T(n, k) = n*((k + n)!)^2/((k + n)*(n!)^2*k!) for n > 0 and T(0, 0) = 1.
1
1, 1, 2, 1, 6, 36, 1, 12, 120, 1200, 1, 20, 300, 4200, 58800, 1, 30, 630, 11760, 211680, 3810240, 1, 42, 1176, 28224, 635040, 13970880, 307359360, 1, 56, 2016, 60480, 1663200, 43908480, 1141620480, 29682132480, 1, 72, 3240, 118800, 3920400, 122316480, 3710266560, 111307996800, 3339239904000
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
T(n, 1) = A002378, T(n, n) = A187535, A355004 (row sums), A271703 (Lah).
Sequence in context: A268371 A318918 A100404 * A320570 A300911 A347899
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jun 15 2022
STATUS
approved