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%I #26 Apr 04 2020 19:18:12
%S 1,1,1,1,1,1,1,2,1,1,1,5,4,1,1,1,13,14,4,1,1,1,38,129,41,7,1,1,1,149,
%T 1980,1981,157,8,1,1,1,703,62611,304495,62616,725,12,1,1,1,4132,
%U 2806490,78322915,78322916,2806508,4196,14,1,1,1,29579,158937213,27033154060,147252447227,27033154065,158937367,29817,21,1,1
%N Triangle read by rows: T(n,k) is the number of simple regular connected bipartite graphs with 2n nodes and degree k, (2 <= k <= n).
%C This sequence can be derived from A133687 and A333159. In particular, if w(n) is the inverse Euler transform of column k of A133687 and s(n) is the inverse Euler transform of column k of A333159, then 2*T(2*n+1,k) = w(2*n+1) + s(2*n+1) and 2*T(2*n,k) = w(2*n) + s(2*n) - w(n) + T(n,k). - _Andrew Howroyd_, Apr 03 2020
%H Andrew Howroyd, <a href="/A008326/b008326.txt">Table of n, a(n) for n = 2..154</a>
%H B. D. McKay and E. Rogoyski, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v2i1n3">Latin squares of order ten</a>, Electron. J. Combinatorics, 2 (1995) #N3.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, 1, 1;
%e 1, 2, 1, 1;
%e 1, 5, 4, 1, 1;
%e 1, 13, 14, 4, 1, 1;
%e 1, 38, 129, 41, 7, 1, 1;
%e 1, 149, 1980, 1981, 157, 8, 1, 1;
%e ...
%Y Columns k=3..7 are A006823, A006824, A006825, A014385, A014387.
%Y Row sums are in A008323.
%Y Cf. A008327, A133687, A333159.
%K nonn,hard,tabl
%O 2,8
%A _Brendan McKay_ and Eric Rogoyski
%E More terms from Eric Rogoyski, May 15 1997
%E Name clarified by _Andrew Howroyd_, Sep 05 2018
%E Terms a(55) and beyond from _Andrew Howroyd_, Apr 03 2020
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