A062740 Number of connected labeled graphs with loops.

1, 2, 4, 32, 608, 23296, 1709056, 238880768, 64396439552, 33943701028864, 35324404321091584, 72994114660256448512, 300460426062916084563968, 2468021884106048216693211136, 40495494119922790159005962469376, 1328011048967552376327692463141552128

Offset: 0

Author

Vladeta Jovovic, Jul 12 2001

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A006125, A226773.

Programs

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 *)

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