A066991 Square array read by descending antidiagonals of number of ways of dividing n*k labeled items into k unlabeled orders with n items in each order.
1, 1, 2, 1, 12, 6, 1, 120, 360, 24, 1, 1680, 60480, 20160, 120, 1, 30240, 19958400, 79833600, 1814400, 720, 1, 665280, 10897286400, 871782912000, 217945728000, 239500800, 5040, 1, 17297280, 8892185702400, 20274183401472000
Offset: 1
Examples
The array begins: n\k| 1 2 3 4 ... -------------------------------------------------------- 1 | 1, 1, 1, 1, ... 2 | 2, 12, 120, 1680, ... 3 | 6, 360, 60480, 19958400, ... 4 | 24, 20160, 79833600, 871782912000, ... 5 | 120, 1814400, 217945728000, 101370917007360000, ... ...
Links
- Paolo Xausa, Table of n, a(n) for n = 1..820 (antidiagonals 1..40 of the array, flattened).
Crossrefs
Programs
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Mathematica
Table[((n-k+1)*k)!/k!, {n, 10}, {k, n, 1, -1}] (* Paolo Xausa, Feb 19 2024 *)
Formula
T(n,k) = (n*k)!/k!.
Extensions
Edited by Paolo Xausa, Feb 19 2024
Comments