

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.


6



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

Table of n, a(n) for n=1..61.


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

Row sums: A052171. Partial row sums: A138107.
Sums of the first m entries of each row: A005993 (m=2), A050927 (m=3), A050929 (m=4).
Sequence in context: A213658 A046575 A154739 * A136042 A268911 A166044
Adjacent sequences: A136561 A136562 A136563 * A136565 A136566 A136567


KEYWORD

nonn,tabf


AUTHOR

Benoit Jubin, Apr 14 2008


EXTENSIONS

More terms from Benoit Jubin and Vladeta Jovovic, Sep 08 2008


STATUS

approved



