A277031 - OEIS

%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