Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #20 Jul 31 2017 12:45:28
%S 1,1,1,5,4,1,1,9,21,16,4,1,1,18,71,108,71,22,4,1,1,27,194,491,557,326,
%T 101,22,4,1,1,43,476,1903,3353,3062,1587,497,111,22,4,1,1,59,1030,
%U 6298,16644,22352,17035,7982,2433,555,111,22,4,1,1,84,2095,18823,72064
%N Array read by rows: T(n,k) is the number of directed multigraphs with loops with n arcs, k vertices, and no vertex of degree 0.
%C Length of the n^th row: 2n.
%F T(n,1) = 1 if n > 0.
%F T(n,2n) = 1 if n > 0.
%F T(n,2n-1) = 4 if n >= 2.
%F T(n,2n-k) = A144047(k) for n large enough (conjecturally, n >= 2k is enough).
%F T(n,2) = (n^3 + 6*n^2 + 11*n - 6)/12 + ((n+2)/4)[n even]. (the bracket means that the second term is added if and only if n is even). - _Benoit Jubin_, Mar 31 2012
%e 1, 1;
%e 1, 5, 4, 1;
%e 1, 9, 21, 16, 4, 1;
%e 1, 18, 71, 108, 71, 22, 4, 1;
%e 1, 27, 194, 491, 557, 326, 101, 22, 4, 1;
%e 1, 43, 476, 1903, 3353, 3062, 1587, 497, 111, 22, 4, 1;
%e 1, 59, 1030, 6298, 16644, 22352, 17035, 7982, 2433, 555, 111, 22, 4, 1;
%Y Row sums: A052171. Partial row sums: A138107.
%Y Sums of the first m entries of each row: A005993 (m=2), A050927 (m=3), A050929 (m=4).
%K nonn,tabf
%O 1,4
%A _Benoit Jubin_, Apr 14 2008
%E More terms from _Benoit Jubin_ and _Vladeta Jovovic_, Sep 08 2008