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.

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

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,2n-1) = 4 if n >= 2.

T(n,2n-k) = 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: A046575 A154739 A321044 * A136042 A268911 A351123

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