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A136564 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.

%I A136564 #20 Jul 31 2017 12:45:28
%S A136564 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 A136564 101,22,4,1,1,43,476,1903,3353,3062,1587,497,111,22,4,1,1,59,1030,
%U A136564 6298,16644,22352,17035,7982,2433,555,111,22,4,1,1,84,2095,18823,72064
%N A136564 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 A136564 Length of the n^th row: 2n.
%F A136564 T(n,1) = 1 if n > 0.
%F A136564 T(n,2n) = 1 if n > 0.
%F A136564 T(n,2n-1) = 4 if n >= 2.
%F A136564 T(n,2n-k) = A144047(k) for n large enough (conjecturally, n >= 2k is enough).
%F A136564 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 A136564 1, 1;
%e A136564 1, 5, 4, 1;
%e A136564 1, 9, 21, 16, 4, 1;
%e A136564 1, 18, 71, 108, 71, 22, 4, 1;
%e A136564 1, 27, 194, 491, 557, 326, 101, 22, 4, 1;
%e A136564 1, 43, 476, 1903, 3353, 3062, 1587, 497, 111, 22, 4, 1;
%e A136564 1, 59, 1030, 6298, 16644, 22352, 17035, 7982, 2433, 555, 111, 22, 4, 1;
%Y A136564 Row sums: A052171. Partial row sums: A138107.
%Y A136564 Sums of the first m entries of each row: A005993 (m=2), A050927 (m=3), A050929 (m=4).
%K A136564 nonn,tabf
%O A136564 1,4
%A A136564 _Benoit Jubin_, Apr 14 2008
%E A136564 More terms from _Benoit Jubin_ and _Vladeta Jovovic_, Sep 08 2008