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Triangle read by rows: T(n,k) is the number of connected k-regular simple graphs on n labeled vertices, (0 <= k < n).
5

%I #12 Sep 02 2019 23:04:26

%S 1,0,1,0,0,1,0,0,3,1,0,0,12,0,1,0,0,60,70,15,1,0,0,360,0,465,0,1,0,0,

%T 2520,19320,19355,3507,105,1,0,0,20160,0,1024380,0,30016,0,1,0,0,

%U 181440,11166120,66462480,66462606,11180820,286884,945,1

%N Triangle read by rows: T(n,k) is the number of connected k-regular simple graphs on n labeled vertices, (0 <= k < n).

%H Andrew Howroyd, <a href="/A324163/b324163.txt">Table of n, a(n) for n = 1..210</a>

%F Column k is the logarithmic transform of column k of A059441.

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 0, 1;

%e 0, 0, 3, 1;

%e 0, 0, 12, 0, 1;

%e 0, 0, 60, 70, 15, 1;

%e 0, 0, 360, 0, 465, 0, 1;

%e 0, 0, 2520, 19320, 19355, 3507, 105, 1;

%e 0, 0, 20160, 0, 1024380, 0, 30016, 0, 1;

%e ...

%Y Column k=2 is A001710(n-1) for n >= 3.

%Y Column k=3 is aerated A004109.

%Y Column k=4 is A272905.

%Y Row sums are A322659.

%Y Cf. A059441 (not necessarily connected), A068934 (unlabeled).

%K nonn,tabl

%O 1,9

%A _Andrew Howroyd_, Sep 02 2019