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, 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
Examples
[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;
Programs
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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);
Formula
T(n, k) = Lah(k + n, n), where Lah denotes the unsigned Lah numbers A271703.