Alois P. Heinz, <a href="/A137916/b137916_2.txt">Table of n, a(n) for n = 0..386</a> (terms n = 151..200 from Andrew Howroyd)

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Andrew Howroyd, Alois P. Heinz, <a href="/A137916/b137916_2.txt">Table of n, a(n) for n = 0..200386</a> (terms 1n = 151..150 200 from Alois P. HeinzAndrew Howroyd)

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Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pseudoforest.html">Pseudoforest</a>.

Wikipedia, <a href="http://en.wikipedia.org/wiki/Pseudoforest">Pseudoforest</a>.

a(n) = Sum_{N = 1..n} ((n!/N! ) * Sum_{n_1 + n_2 + ... + n_N = n} Product_{i = 1..N} ( A057500(n_i) / n_i! ) ). [V. F. Kolchin p. 31, (1.4.2)] replacing numerator terms n_i^(n_i-2) by A057500(n_i).

E.g.f.: exp(B(T(x))) where B(x) = (log(1/(1-x))-x-x^2/2)/2 and T(x) is the e.g.f. for A000169 (labeled rooted trees). - Geoffrey Critzer, Jan 24 2012

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Diagonal of A144228.

Row sums of A106239.

Row sums of A106239.

Diagonal of A144228.

Choosable simple graphs are counted by A133686, covering A367869.

`A129271 A133686 counts connected choosable simple graphs, unlabeled A005703covering A367869.

Cf. A001434, A006649, `A014068, `A053530, A116508, A129271, A134964, A140638, A367862, `A367863, A368601, `A369141, A369191.

Also the number of labeled simple graphs with n vertices and n edges such that it is possible to choose a different vertex from each edge (choosable). The version without the choice condition is A116508, covering A367863. - Gus Wiseman, Jan 25 2024

{} . . {12-,13-,23} {12-,13-,14-,23}

{12-,13-,14-,24}

{12-,13-,14-,34}

{12-,13-,23-,24}

{12-,13-,23-,34}

{12-,13-,24-,34}

{12-,14-,23-,24}

{12-,14-,23-,34}

{12-,14-,24-,34}

{12-,23-,24-,34}

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{13-,14-,23-,34}

{13-,14-,24-,34}

{13-,23-,24-,34}

{14-,23-,24-,34}