cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A060516 #7 Apr 29 2019 16:30:38
%S A060516 1,1,5,26,328,9700,711836,111817032,35130791054,21495893690664,
%T A060516 25409892375220474,58052821046020873856,257486314335782707924088,
%U A060516 2230295461268044025586193298,37948847404292424846290915818844
%N A060516 Number of series-reduced (or homeomorphically irreducible) graphs with loops on n labeled nodes.
%C A060516 Conjecture: the number of connected graphs of this type is 1, 1, 4, 13, 203, 7754, ... (n>=0). - _R. J. Mathar_, Apr 29 2019
%D A060516 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983.
%F A060516 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!.
%Y A060516 Cf. A003514. Row sums of A060517.
%K A060516 easy,nonn
%O A060516 0,3
%A A060516 _Vladeta Jovovic_, Mar 24 2001