A089479 Triangle T(n,k) read by rows, where T(n,k) = number of times the permanent of a real n X n (0,1)-matrix takes the value k, for n >= 0, 0 <= k <= n!.
0, 1, 1, 1, 9, 6, 1, 265, 150, 69, 18, 9, 0, 1, 27713, 13032, 10800, 4992, 4254, 1440, 1536, 576, 648, 24, 288, 96, 48, 0, 72, 0, 0, 0, 16, 0, 0, 0, 0, 0, 1, 10363361, 3513720, 4339440, 2626800, 3015450, 1451400, 1872800, 962400, 1295700, 425400, 873000
Offset: 0
Examples
Triangle begins:
0, 1;
1, 1;
9, 6, 1;
265, 150, 69, 18, 9, 0, 1;
27713, 13032, 10800, 4992, 4254, 1440, 1536, 576, 648, 24, 288,
96, 48, 0, 72, 0, 0, 0, 16, 0, 0, 0, 0, 0, 1;
...
Links
- Hugo Pfoertner, Table of n, a(n) for n = 0..159 (rows 0..5, flattened)
Crossrefs
T(n,0) = A088672(n), T(n,1) = A089482(n). The n-th row of the table contains A087983(n) nonzero entries. For n>2 A089477(n) gives the position of the first zero entry in the n-th row.
Formula
From Geoffrey Critzer, Dec 20 2023: (Start)
Sum_{k=1..n!} T(n,k) = A227414(n).
For n>2, T(n,n!-(n-1)!) = n^2, the number of matrices with exactly one 0 entry. (End)
Extensions
Edited by Alois P. Heinz, Dec 20 2023
Comments