

A322661


Number of graphs with loops spanning n labeled vertices.


2



1, 1, 5, 45, 809, 28217, 1914733, 254409765, 66628946641, 34575388318705, 35680013894626133, 73392583417010454429, 301348381381966079690489, 2471956814761996896091805993, 40530184362443281653842556898237, 1328619783326799871943604598592805525
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OFFSET

0,3


COMMENTS

The span of a graph is the union of its edges.


LINKS

Table of n, a(n) for n=0..15.


FORMULA

Exponential transform of A062740, if we assume A062740(1) = 1.
Inverse binomial transform of A006125(n+1) = 2^binomial(n+1,2).


EXAMPLE

The a(2) = 5 edgesets:
{{1,2}}
{{1,1},{1,2}}
{{1,1},{2,2}}
{{1,2},{2,2}}
{{1,1},{1,2},{2,2}}


MATHEMATICA

Table[Sum[(1)^(nk)*Binomial[n, k]*2^Binomial[k+1, 2], {k, 0, n}], {n, 10}]
(* second program *)
Table[Select[Expand[Product[1+x[i]*x[j], {j, n}, {i, j}]], And@@Table[!FreeQ[#, x[i]], {i, n}]&]/.x[_]>1, {n, 7}]


CROSSREFS

Cf. A000666, A006125, A006129, A054921, A062740, A116539, A320461, A322635.
Sequence in context: A243951 A290941 A211051 * A191962 A326650 A323572
Adjacent sequences: A322658 A322659 A322660 * A322662 A322663 A322664


KEYWORD

nonn


AUTHOR

Gus Wiseman, Dec 22 2018


STATUS

approved



