A060516 Number of series-reduced (or homeomorphically irreducible) graphs with loops on n labeled nodes.

1, 1, 5, 26, 328, 9700, 711836, 111817032, 35130791054, 21495893690664, 25409892375220474, 58052821046020873856, 257486314335782707924088, 2230295461268044025586193298, 37948847404292424846290915818844

Offset: 0

Author

Vladeta Jovovic, Mar 24 2001

Keywords

• easy
• nonn

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.

Crossrefs

Cf. A003514. Row sums of A060517.

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!.