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A322661 Number of graphs with loops spanning n labeled vertices. 14
1, 1, 5, 45, 809, 28217, 1914733, 254409765, 66628946641, 34575388318705, 35680013894626133, 73392583417010454429, 301348381381966079690489, 2471956814761996896091805993, 40530184362443281653842556898237, 1328619783326799871943604598592805525 (list; graph; refs; listen; history; text; internal format)
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 edge-sets:

  {{1,2}}

  {{1,1},{1,2}}

  {{1,1},{2,2}}

  {{1,2},{2,2}}

  {{1,1},{1,2},{2,2}}

MATHEMATICA

Table[Sum[(-1)^(n-k)*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

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Last modified May 18 16:07 EDT 2021. Contains 343995 sequences. (Running on oeis4.)