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A351263 Triangle read by rows: T(n,k) is the number of oriented graphs on n labeled nodes whose underlying graph is k-regular, k = 0..n-1.

%I A351263 #11 Apr 16 2022 05:47:55
%S A351263 1,1,2,1,0,8,1,12,48,64,1,0,384,0,1024,1,120,4480,35840,61440,32768,1,
%T A351263 0,59520,0,7618560,0,2097152,1,1680,897792,79278080,1268449280,
%U A351263 3677356032,1761607680,268435456,1,0,15368192,0,268535070720,0,4028679323648,0,68719476736
%N A351263 Triangle read by rows: T(n,k) is the number of oriented graphs on n labeled nodes whose underlying graph is k-regular, k = 0..n-1.
%C A351263 The sum of the in-degree and out-degree at each node is k.
%H A351263 Andrew Howroyd, <a href="/A351263/b351263.txt">Table of n, a(n) for n = 1..300</a> (rows 1..24)
%F A351263 T(n,k) = A059441(n,k)*2^(n*k/2). - _Pontus von Brömssen_, Apr 04 2022
%e A351263 Triangle begins:
%e A351263   1;
%e A351263   1,   2;
%e A351263   1,   0,     8;
%e A351263   1,  12,    48,    64;
%e A351263   1,   0,   384,     0,    1024;
%e A351263   1, 120,  4480, 35840,   61440, 32768;
%e A351263   1,   0, 59520,     0, 7618560,     0, 2097152;
%e A351263   ...
%Y A351263 Row sums are A351264.
%Y A351263 Main diagonal is A006125.
%Y A351263 The unlabeled version is A350912.
%Y A351263 Cf. A059441 (graphs).
%K A351263 nonn,tabl
%O A351263 1,3
%A A351263 _Andrew Howroyd_, Feb 05 2022