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%I #14 Oct 28 2020 10:18:27
%S 1,0,1,0,1,1,0,5,0,1,0,20,3,0,1,0,109,10,0,0,1,0,668,44,7,0,0,1,0,
%T 4801,210,28,0,0,0,1,0,38894,1320,90,15,0,0,0,1,0,353811,8439,554,75,
%U 0,0,0,0,1,0,3561512,63404,3542,310,31,0,0,0,0,1,0,39374609,517418,23298,1276,198,0,0,0,0,0,1
%N Number T(n,k) of permutations of [n] where the minimal cyclic distance between elements of the same cycle equals k (k=n for the identity permutation in S_n); triangle T(n,k), n>=0, 0<=k<=n, read by rows.
%H Alois P. Heinz, <a href="/A277031/b277031.txt">Rows n = 0..12, flattened</a>
%H Per Alexandersson et al., <a href="https://mathoverflow.net/questions/168885">d-regular partitions and permutations</a>, MathOverflow, 2014
%e T(3,1) = 5: (1,2,3), (1,3,2), (1)(2,3), (1,2)(3), (1,3)(2).
%e T(3,3) = 1: (1)(2)(3).
%e Triangle T(n,k) begins:
%e 1;
%e 0, 1;
%e 0, 1, 1;
%e 0, 5, 0, 1;
%e 0, 20, 3, 0, 1;
%e 0, 109, 10, 0, 0, 1;
%e 0, 668, 44, 7, 0, 0, 1;
%e 0, 4801, 210, 28, 0, 0, 0, 1;
%e 0, 38894, 1320, 90, 15, 0, 0, 0, 1;
%e 0, 353811, 8439, 554, 75, 0, 0, 0, 0, 1;
%e 0, 3561512, 63404, 3542, 310, 31, 0, 0, 0, 0, 1;
%e ...
%Y Columns k=0-1 give: A000007, A277032.
%Y Row sums give A000142.
%Y T(2n,n) = A255047(n) = A000225(n) for n>0.
%Y Cf. A239145, A263757, A276974.
%K nonn,tabl
%O 0,8
%A _Alois P. Heinz_, Sep 25 2016
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