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%I #17 Oct 28 2020 10:18:56
%S 1,0,1,0,1,1,0,4,1,1,0,19,3,1,1,0,103,12,3,1,1,0,651,54,10,3,1,1,0,
%T 4702,281,42,10,3,1,1,0,38413,1652,203,37,10,3,1,1,0,350559,11017,
%U 1086,166,37,10,3,1,1,0,3539511,81665,6564,857,151,37,10,3,1,1,0,39196758,669948,44265,4900,726,151,37,10,3,1,1
%N Number T(n,k) of permutations of [n] where the minimal 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="/A276974/b276974.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) = 4: (1,2,3), (1,3,2), (1)(2,3), (1,2)(3).
%e T(3,2) = 1: (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, 4, 1, 1;
%e 0, 19, 3, 1, 1;
%e 0, 103, 12, 3, 1, 1;
%e 0, 651, 54, 10, 3, 1, 1;
%e 0, 4702, 281, 42, 10, 3, 1, 1;
%e 0, 38413, 1652, 203, 37, 10, 3, 1, 1;
%e 0, 350559, 11017, 1086, 166, 37, 10, 3, 1, 1;
%e 0, 3539511, 81665, 6564, 857, 151, 37, 10, 3, 1, 1;
%e ...
%Y Columns k=0-1 give: A000007, A276975.
%Y Row sums give A000142.
%Y T(2n,n) = A138378(n) = A005493(n-1) for n>0.
%Y Cf. A239145, A263757, A277031.
%K nonn,tabl
%O 0,8
%A _Alois P. Heinz_, Sep 23 2016