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