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A062740 Number of connected labeled graphs with loops. 2
1, 2, 4, 32, 608, 23296, 1709056, 238880768, 64396439552, 33943701028864, 35324404321091584, 72994114660256448512, 300460426062916084563968, 2468021884106048216693211136, 40495494119922790159005962469376 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..80

FORMULA

E.g.f.: 1+log( Sum_{n >= 0} 2^binomial(n+1, 2)*x^n/n! ).

E.g.f.: A(2*x) where A(x) is the e.g.f. for A001187. - Geoffrey Critzer, Feb 01 2014

MAPLE

logtr:= proc(p) local b; b:= proc(n) option remember; if n=0 then 1 else p(n)- add(k *binomial(n, k) *p(n-k) *b(k), k=1..n-1)/n fi end end:

a:= logtr(n-> 2^binomial(n+1, 2)):

seq(a(n), n=0..20);  # Alois P. Heinz, Feb 01 2014

MATHEMATICA

nn=14; g=Sum[2^Binomial[n, 2](2x)^n/n!, {n, 0, nn}]; Range[0, nn]!CoefficientList[Series[Log[g]+1, {x, 0, nn}], x] (* Geoffrey Critzer, Feb 01 2014 *)

CROSSREFS

Cf. A006125, A226773.

Sequence in context: A304862 A118992 A012509 * A122214 A122216 A100117

Adjacent sequences:  A062737 A062738 A062739 * A062741 A062742 A062743

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jul 12 2001

STATUS

approved

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Last modified October 19 08:15 EDT 2018. Contains 316337 sequences. (Running on oeis4.)