A377597 Table read by antidiagonals: T(n,k) = (n*k)!/(n^k*k!), n >=1, k >= 0.
1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 15, 40, 6, 1, 1, 105, 2240, 1260, 24, 1, 1, 945, 246400, 1247400, 72576, 120, 1, 1, 10395, 44844800, 3405402000, 1743565824, 6652800, 720, 1, 1, 135135, 12197785600, 19799007228000, 162193467211776, 4940103168000, 889574400, 5040, 1
Offset: 1
Examples
The table begins: n\k| 0 1 2 3 4 5 ---+----------------------------------------------------------- 1 | 1 1 1 1 1 1 2 | 1 1 3 15 105 945 3 | 1 2 40 2240 246400 44844800 4 | 1 6 1260 1247400 3405402000 19799007228000 5 | 1 24 72576 1743565824 162193467211776 41363226782215962624 For example T(2,5) = (2*5)!/(2^5*5!) = 10!/(32*5!) = 945.
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