A121227 Number of labeled multigraphs with loops and with n edges and no vertex of degree 0.

1, 2, 14, 150, 2210, 41642, 956878, 25955630, 811819826, 28764498386, 1138755852990, 49817190098694, 2386544217733906, 124257113538066522, 6986465328614267742, 421887743219324342110, 27231714819135144778722, 1871047822756547798671074

Offset

0,2

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..75

Formula

a(n) = Sum_{k=0..2*n} binomial(k*(k+1)/2+n-1, n)*(Sum_{r=k..2*n} binomial(r, k)*(-1)^(r-k)). - Andrew Howroyd, Sep 15 2018

Maple

seq(sum(binomial(m*(m+1)/2+n-1, n)/2^(m+1), m=0..infinity), n=0..10);

Prog

(PARI) a(n)={sum(k=0, 2*n, binomial(k*(k+1)/2+n-1, n)*sum(r=k, 2*n, binomial(r, k)*(-1)^(r-k)) )} \\ Andrew Howroyd, Sep 15 2018

Crossrefs

Row n=2 of A331315.

Unlabeled analog is A007717.

Sequence in context: A333592 A087132 A036079 * A250916 A354751 A211398

Adjacent sequences: A121224 A121225 A121226 * A121228 A121229 A121230

Keyword

easy,nonn

Author

Vladeta Jovovic, Sep 06 2006

Status

approved