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

0,2

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 * A336832 A122214 A122216

Adjacent sequences: A062737 A062738 A062739 * A062741 A062742 A062743

Keyword

easy,nonn

Author

Vladeta Jovovic, Jul 12 2001

Status

approved