cp's OEIS Frontend

A371633 Number of ways to choose a simple labeled graph on [n], then partition the vertex set into independent sets, then choose a vertex from each independent set.

%I A371633 #14 Jun 07 2024 14:18:50
%S A371633 1,1,4,35,740,34629,3581894,802937479,386655984648,396751196145673,
%T A371633 862046936883049482,3946154005780155709451,37896676657907955726032908,
%U A371633 760791471852690599411320471565,31830237745009483676211065390546958,2768049771339996987073597682850993569807
%N A371633 Number of ways to choose a simple labeled graph on [n], then partition the vertex set into independent sets, then choose a vertex from each independent set.
%C A371633 An independent set is a set of vertices in a graph, no two of which are adjacent.
%H A371633 R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/pubs/pubfiles/37.pdf">Exponential structures</a>
%F A371633 Sum_{n>=0} a(n)*x^n/A011266(n) = exp(f(x)) where f(x) = Sum_{n>=1} n*x^n/A011266(n).
%t A371633 nn = 14; B[n_] := n! 2^Binomial[n, 2];ggf[egf_] := Normal[Series[egf, {x, 0, nn}]] /.Table[x^i -> x^i/2^Binomial[i, 2], {i, 0, nn}];Table[B[n], {n, 0, nn}] CoefficientList[Series[Exp[ggf[x Exp[x]]], {x, 0, nn}], x]
%Y A371633 Cf. A000248, A240936, A058843, A011266.
%K A371633 nonn
%O A371633 0,3
%A A371633 _Geoffrey Critzer_, Jun 06 2024