

A327367


Number of labeled simple graphs with n vertices, at least one of which is isolated.


1



0, 1, 1, 4, 23, 256, 5319, 209868, 15912975, 2343052576, 675360194287, 383292136232380, 430038382710483623, 956430459603341708896, 4224538833207707658410103, 37106500399796746894085512140, 648740170822904504303462104598943
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OFFSET

0,4


LINKS

Table of n, a(n) for n=0..16.


FORMULA

a(n) = A006125(n)  A006129(n).


MAPLE

b:= proc(n) option remember; `if`(n=0, 1,
2^binomial(n, 2)add(b(k)*binomial(n, k), k=0..n1))
end:
a:= n> 2^(n*(n1)/2)b(n):
seq(a(n), n=0..17); # Alois P. Heinz, Sep 04 2019


MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#!=Range[n]&]], {n, 0, 5}]


PROG

(PARI) b(n) = sum(k=0, n, (1)^(nk)*binomial(n, k)*2^binomial(k, 2)); \\ A006129
a(n) = 2^(n*(n1)/2)  b(n); \\ Michel Marcus, Sep 05 2019


CROSSREFS

The unlabeled version is A000088(n  1).
Labeled graphs with no isolated vertices are A006129.
Covering graphs with at least one endpoint are A327227.
Cf. A006125, A006129, A054592, A245797, A327103, A327105.
Sequence in context: A123637 A293510 A234595 * A303652 A130890 A138578
Adjacent sequences: A327364 A327365 A327366 * A327368 A327369 A327370


KEYWORD

nonn


AUTHOR

Gus Wiseman, Sep 04 2019


STATUS

approved



