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Triangle read by rows: T(n,k) is the number of k-regular digraphs on n unlabeled nodes, k = 0..n-1.
7

%I #8 Jan 29 2022 20:13:46

%S 1,1,1,1,1,1,1,2,2,1,1,2,5,2,1,1,4,23,23,4,1,1,4,92,415,92,4,1,1,7,

%T 624,19041,19041,624,7,1,1,8,5021,1104045,6510087,1104045,5021,8,1,1,

%U 12,47034,79818336,2983458766,2983458766,79818336,47034,12,1

%N Triangle read by rows: T(n,k) is the number of k-regular digraphs on n unlabeled nodes, k = 0..n-1.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 2, 2, 1;

%e 1, 2, 5, 2, 1;

%e 1, 4, 23, 23, 4, 1;

%e 1, 4, 92, 415, 92, 4, 1;

%e 1, 7, 624, 19041, 19041, 624, 7, 1;

%e ...

%Y Columns k=0..6 are A000012, A002865, A219889, A219890, A219891, A219892, A219893.

%Y Row sums are A350911.

%Y Cf. A051031 (graphs), A329228 (semi-regular), A350912.

%K nonn,tabl

%O 1,8

%A _Andrew Howroyd_, Jan 29 2022