cp's OEIS Frontend

A377597 Table read by antidiagonals: T(n,k) = (n*k)!/(n^k*k!), n >=1, k >= 0.

%I A377597 #14 Nov 04 2024 22:28:09
%S A377597 1,1,1,1,1,1,1,3,2,1,1,15,40,6,1,1,105,2240,1260,24,1,1,945,246400,
%T A377597 1247400,72576,120,1,1,10395,44844800,3405402000,1743565824,6652800,
%U A377597 720,1,1,135135,12197785600,19799007228000,162193467211776,4940103168000,889574400,5040,1
%N A377597 Table read by antidiagonals: T(n,k) = (n*k)!/(n^k*k!), n >=1, k >= 0.
%C A377597 This is the number of permutations in S_{k*n} that consist of k disjoint n-cycles.
%e A377597 The table begins:
%e A377597 n\k| 0  1     2          3               4                    5
%e A377597 ---+-----------------------------------------------------------
%e A377597  1 | 1  1     1          1               1                    1
%e A377597  2 | 1  1     3         15             105                  945
%e A377597  3 | 1  2    40       2240          246400             44844800
%e A377597  4 | 1  6  1260    1247400      3405402000       19799007228000
%e A377597  5 | 1 24 72576 1743565824 162193467211776 41363226782215962624
%e A377597 For example T(2,5) = (2*5)!/(2^5*5!) = 10!/(32*5!) = 945.
%Y A377597 Cf. A001147 (row 2), A052502 (row 3), A060706 (row 4), A052504 (row 5), A110468 (col 2).
%Y A377597 Cf. A368213.
%K A377597 nonn,tabl
%O A377597 1,8
%A A377597 _Peter Kagey_, Nov 02 2024