

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.


7



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, 101, 22, 4, 1, 1, 43, 476, 1903, 3353, 3062, 1587, 497, 111, 22, 4, 1, 1, 59, 1030, 6298, 16644, 22352, 17035, 7982, 2433, 555, 111, 22, 4, 1, 1, 84, 2095, 18823, 72064
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OFFSET

1,4


COMMENTS

Length of the n^th row: 2n.


LINKS



FORMULA

T(n,1) = 1 if n > 0.
T(n,2n) = 1 if n > 0.
T(n,2n1) = 4 if n >= 2.
T(n,2nk) = A144047(k) for n large enough (conjecturally, n >= 2k is enough).
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


EXAMPLE

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, 101, 22, 4, 1;
1, 43, 476, 1903, 3353, 3062, 1587, 497, 111, 22, 4, 1;
1, 59, 1030, 6298, 16644, 22352, 17035, 7982, 2433, 555, 111, 22, 4, 1;


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



EXTENSIONS



STATUS

approved



