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%I #26 Feb 17 2022 13:34:35
%S 1,2,1,6,2,2,24,9,6,6,120,44,24,24,24,720,265,160,120,120,120,5040,
%T 1854,1140,720,720,720,720,40320,14833,8988,6300,5040,5040,5040,5040,
%U 362880,133496,80864,58464,40320,40320,40320,40320,40320
%N Triangle read by rows: T(n,k) is the number of permutations in S_n for which all cycles are length k or greater.
%H Peter Kagey, <a href="/A333726/b333726.txt">Table of n, a(n) for n = 1..10011</a> (first 141 rows, flattened)
%H Steven Finch, <a href="http://arxiv.org/abs/2202.07621">Second best, Third worst, Fourth in line</a>, arxiv:2202.07621 [math.CO], 2022.
%F T(n,k) = 0 when n < k,
%F T(n,k) = (n-1)! when n = k, and otherwise
%F T(n,k) = (n-1) * T(n-1, k) + A068424(n-1, k-1) * T(n-k, k).
%e Triangle begins:
%e n\k| 1 2 3 4 5 6 7 8 9
%e ---+--------------------------------------------------------
%e 1| 1
%e 2| 2 1
%e 3| 6 2 2
%e 4| 24 9 6 6
%e 5| 120 44 24 24 24
%e 6| 720 265 160 120 120 120
%e 7| 5040 1854 1140 720 720 720 720
%e 8| 40320 14833 8988 6300 5040 5040 5040 5040
%e 9| 362880 133496 80864 58464 40320 40320 40320 40320 40320
%Y Columns 1-4: A000142, A000166, A038205, A047865.
%Y Cf. A068424.
%K nonn,tabl
%O 1,2
%A _Peter Kagey_, Apr 23 2020
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