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%I #20 Apr 04 2020 14:39:43
%S 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,4,6,4,1,1,1,1,4,14,14,
%T 4,1,1,1,1,7,41,130,41,7,1,1,1,1,8,157,1981,1981,157,8,1,1,1,1,12,725,
%U 62616,304496,62616,725,12,1,1,1,1,14,4196,2806508,78322916
%N Triangle read by rows: T(n,k) is the number of simple regular bipartite graphs with 2n nodes and degree k, (0 <= k <= n).
%C This sequence can be derived from A008326 by Euler transform. - _Andrew Howroyd_, Apr 03 2020
%H Andrew Howroyd, <a href="/A008327/b008327.txt">Table of n, a(n) for n = 0..189</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.
%F Column k is the Euler transform of column k of A008326. - _Andrew Howroyd_, Apr 03 2020
%e Triangle begins:
%e 1,
%e 1, 1,
%e 1, 1, 1,
%e 1, 1, 1, 1,
%e 1, 1, 2, 1, 1,
%e 1, 1, 2, 2, 1, 1,
%e 1, 1, 4, 6, 4, 1, 1;
%e 1, 1, 4, 14, 14, 4, 1, 1;
%e 1, 1, 7, 41, 130, 41, 7, 1, 1;
%e 1, 1, 8, 157, 1981, 1981, 157, 8, 1, 1;
%e ...
%Y Column k=0..5 are A000012, A000012, A002865, A008325, A333730, A333731.
%Y Row sums are A008324.
%Y Cf. A051031, A008326, A087114, A133687, A333159.
%K nonn,tabl,nice
%O 0,13
%A _Brendan McKay_
%E More terms from Eric Rogoyski, May 15 1997
%E Name clarified by _Andrew Howroyd_, Sep 05 2018
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