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A121227
Number of labeled multigraphs with loops and with n edges and no vertex of degree 0.
2
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 06 2006
STATUS
approved