login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A060516
Number of series-reduced (or homeomorphically irreducible) graphs with loops on n labeled nodes.
12
1, 1, 5, 26, 328, 9700, 711836, 111817032, 35130791054, 21495893690664, 25409892375220474, 58052821046020873856, 257486314335782707924088, 2230295461268044025586193298, 37948847404292424846290915818844
OFFSET
0,3
COMMENTS
Conjecture: the number of connected graphs of this type is 1, 1, 4, 13, 203, 7754, ... (n>=0). - R. J. Mathar, Apr 29 2019
REFERENCES
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
FORMULA
E.g.f. : (1 + x)^( - 1/2) * exp( - x/2 - x^2/4) * Sum_{k=0..inf} 2^binomial(k + 1, 2) * exp( - x * k^2/(2 * (1 + x)) + x * k/2) * x^k/k!.
CROSSREFS
Cf. A003514. Row sums of A060517.
Sequence in context: A279738 A106296 A295114 * A077537 A140423 A324419
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Mar 24 2001
STATUS
approved