A333158 - OEIS

%I #5 Mar 09 2020 21:18:38

%S 1,0,1,1,1,1,1,1,0,2,0,1,1,3,8,8,3,1,1,0,38,0,38,0,1,1,15,208,730,730,

%T 208,15,1,1,0,1348,0,20670,0,1348,0,1,1,105,10126,188790,781578,

%U 781578,188790,10126,105,1,1,0,86174,0,37885204,0,37885204,0,86174,0,1

%N Irregular triangle read by rows: T(n,k) is the number of k-regular graphs on n labeled nodes with loops allowed, n >= 1, 0 <= k <= n + 1.

%C A loop adds 2 to the degree of its vertex.

%F T(n,k) = T(n, n+1-k).

%e Triangle begins:

%e   1,   0,     1;

%e   1,   1,     1,      1;

%e   1,   0,     2,      0,      1;

%e   1,   3,     8,      8,      3,      1;

%e   1,   0,    38,      0,     38,      0,      1;

%e   1,  15,   208,    730,    730,    208,     15,     1;

%e   1,   0,  1348,      0,  20670,      0,   1348,     0,   1;

%e   1, 105, 10126, 188790, 781578, 781578, 188790, 10126, 105, 1;

%e   ...

%Y Row sums are A322635.

%Y Columns k=0..4 are A000012, A123023, A108246, A110039 (with interspersed zeros), A228697.

%Y Cf. A059441, A333157.

%K nonn,tabf

%O 1,10

%A _Andrew Howroyd_, Mar 09 2020