A370165 Number of labeled loop-graphs covering n vertices without a non-loop edge with loops at both ends.
1, 1, 4, 29, 400, 10289, 496548, 45455677, 7983420736, 2716094133313, 1803251169342820, 2348787270663723581, 6024912118926389490448, 30516957491540079828757553, 305811332460677494410532494660, 6071677788061208810793717466942237
Offset: 0
Keywords
Examples
The a(3) = 29 loop-graphs (loops shown as singletons):
{1,23} {1,2,3} {1,2,13,23}
{2,13} {1,2,13} {1,3,12,23}
{3,12} {1,2,23} {2,3,12,13}
{12,13} {1,3,12} {1,12,13,23}
{12,23} {1,3,23} {2,12,13,23}
{13,23} {2,3,12} {3,12,13,23}
{2,3,13}
{1,12,13}
{1,12,23}
{1,13,23}
{2,12,13}
{2,12,23}
{2,13,23}
{3,12,13}
{3,12,23}
{3,13,23}
{12,13,23}
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..80
Crossrefs
The non-covering version is A079491.
Programs
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Mathematica
Table[Length[Select[Subsets[Subsets[Range[n],{1,2}]], Union@@#==Range[n]&&!MatchQ[#, {_,{x_},_,{y_},_,{x_,y_},_}]&]],{n,0,5}] -
PARI
seq(n)={Vec(serlaplace(sum(k=0, n, exp((2^k-1)*x + O(x*x^n))*2^(k*(k-1)/2)*x^k/k!)))} \\ Andrew Howroyd, Feb 20 2024
Formula
Inverse binomial transform of A079491.
E.g.f.: Sum_{k >= 0} exp((2^k-1)*x)*2^(k*(k-1)/2)*x^k/k!. - Andrew Howroyd, Feb 20 2024
Comments