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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!.

%I A089479 #30 Sep 20 2024 07:48:39
%S A089479 0,1,1,1,9,6,1,265,150,69,18,9,0,1,27713,13032,10800,4992,4254,1440,
%T A089479 1536,576,648,24,288,96,48,0,72,0,0,0,16,0,0,0,0,0,1,10363361,3513720,
%U A089479 4339440,2626800,3015450,1451400,1872800,962400,1295700,425400,873000
%N 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!.
%C A089479 The last element of each row is 1, corresponding to the n X n "all 1" matrix with permanent = n!. The first 4 rows were provided by _Wouter Meeussen_. The 6th row was computed by _Gordon F. Royle_: 13906734081, 2722682160, 4513642920, 3177532800, 4466769300, 2396826720, 3710999520, 2065521600, 3253760550, 1468314000, 2641593600, 1350475200, 2210277600, 1034061120,... .
%H A089479 Hugo Pfoertner, <a href="/A089479/b089479.txt">Table of n, a(n) for n = 0..159</a> (rows 0..5, flattened)
%F A089479 From _Geoffrey Critzer_, Dec 20 2023: (Start)
%F A089479 Sum_{k=1..n!} T(n,k) = A227414(n).
%F A089479 For n>2, T(n,n!-(n-1)!) = n^2, the number of matrices with exactly one 0 entry. (End)
%e A089479 Triangle begins:
%e A089479     0,     1;
%e A089479     1,     1;
%e A089479     9,     6,     1;
%e A089479   265,   150,    69,   18,    9,    0,    1;
%e A089479 27713, 13032, 10800, 4992, 4254, 1440, 1536, 576, 648, 24, 288,
%e A089479                    96, 48, 0, 72, 0, 0, 0, 16, 0, 0, 0, 0, 0, 1;
%e A089479   ...
%Y A089479 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.
%Y A089479 Cf. A089480 (occurrence counts for permanents of non-singular (0,1)-matrices), A089481 (occurrence counts for permanents of singular (0,1)-matrices).
%Y A089479 Cf. A000290, A038507 (row lengths), A002416 (row sums).
%Y A089479 Cf. A036781, A089478.
%K A089479 nonn,tabf
%O A089479 0,5
%A A089479 _Hugo Pfoertner_, Nov 05 2003
%E A089479 Edited by _Alois P. Heinz_, Dec 20 2023