cp's OEIS Frontend

A277031 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.

%I A277031 #14 Oct 28 2020 10:18:27
%S A277031 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 A277031 4801,210,28,0,0,0,1,0,38894,1320,90,15,0,0,0,1,0,353811,8439,554,75,
%U A277031 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 A277031 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 A277031 Alois P. Heinz, <a href="/A277031/b277031.txt">Rows n = 0..12, flattened</a>
%H A277031 Per Alexandersson et al., <a href="https://mathoverflow.net/questions/168885">d-regular partitions and permutations</a>, MathOverflow, 2014
%e A277031 T(3,1) = 5: (1,2,3), (1,3,2), (1)(2,3), (1,2)(3), (1,3)(2).
%e A277031 T(3,3) = 1: (1)(2)(3).
%e A277031 Triangle T(n,k) begins:
%e A277031   1;
%e A277031   0,       1;
%e A277031   0,       1,     1;
%e A277031   0,       5,     0,    1;
%e A277031   0,      20,     3,    0,   1;
%e A277031   0,     109,    10,    0,   0,  1;
%e A277031   0,     668,    44,    7,   0,  0, 1;
%e A277031   0,    4801,   210,   28,   0,  0, 0, 1;
%e A277031   0,   38894,  1320,   90,  15,  0, 0, 0, 1;
%e A277031   0,  353811,  8439,  554,  75,  0, 0, 0, 0, 1;
%e A277031   0, 3561512, 63404, 3542, 310, 31, 0, 0, 0, 0, 1;
%e A277031   ...
%Y A277031 Columns k=0-1 give: A000007, A277032.
%Y A277031 Row sums give A000142.
%Y A277031 T(2n,n) = A255047(n) = A000225(n) for n>0.
%Y A277031 Cf. A239145, A263757, A276974.
%K A277031 nonn,tabl
%O A277031 0,8
%A A277031 _Alois P. Heinz_, Sep 25 2016