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%I #15 Mar 23 2020 21:10:05
%S 1,1,1,1,0,0,1,1,1,0,1,0,1,0,0,1,1,2,1,0,0,1,0,2,0,1,0,0,1,1,3,4,5,1,
%T 0,0,1,0,3,0,10,0,1,0,0,1,1,4,9,26,28,17,1,0,0,1,0,4,0,47,0,97,0,1,0,
%U 0,1,1,5,17,91,291,639,359,71,1,0,0,1,0,5,0,149,0,2789,0,1635,0,1,0,0
%N Array read by antidiagonals: T(n,k) is the number of connected k-regular multigraphs on n unlabeled nodes, loops allowed, n >= 0, k >= 0.
%C This sequence can be derived from A167625 by inverse Euler transform.
%H Andrew Howroyd, <a href="/A333397/b333397.txt">Table of n, a(n) for n = 0..405</a> (first 28 antidiagonals)
%F Column k is the inverse Euler transform of column k of A167625.
%e Array begins:
%e =========================================================
%e n\k | 0 1 2 3 4 5 6 7 8
%e ----+----------------------------------------------------
%e 0 | 1 1 1 1 1 1 1 1 1 ...
%e 1 | 1 0 1 0 1 0 1 0 1 ...
%e 2 | 0 1 1 2 2 3 3 4 4 ...
%e 3 | 0 0 1 0 4 0 9 0 17 ...
%e 4 | 0 0 1 5 10 26 47 91 149 ...
%e 5 | 0 0 1 0 28 0 291 0 1934 ...
%e 6 | 0 0 1 17 97 639 2789 12398 44821 ...
%e 7 | 0 0 1 0 359 0 35646 0 1631629 ...
%e 8 | 0 0 1 71 1635 40264 622457 8530044 89057367 ...
%e 9 | 0 0 1 0 8296 0 14019433 0 6849428873 ...
%e ...
%Y Columns k=3..8 (with interspersed 0's for odd k) are: A005967, A085549, A129430, A129432, A129434, A129436.
%Y Cf. A167625 (not necessarily connected), A322115 (not necessarily regular), A328682 (loopless), A333330.
%K nonn,tabl
%O 0,18
%A _Andrew Howroyd_, Mar 18 2020