A001188 Number of even graphs with n edges.

1, 2, 8, 60, 672, 9953, 184557, 4142631, 109813842, 3373122370, 118280690398, 4678086540493, 206625802351035, 10107719377251109, 543762148079927802, 31975474310851749920, 2044501883873268414092, 141485408653554069693421

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) appears to be [A060639(n) + 1] / 2. - Ralf Stephan, Aug 21 2004

References

• D. G. Cantor, personal communication.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..50
• E. N. Gilbert, Enumeration of labelled graphs, Canad. J. Math., 8 (1956), 405-411.
• E. N. Gilbert, Enumeration of labelled graphs (Annotated scanned copy)
• R. W. Robinson, First 50 terms of A1187 and A1188

Programs

Maple

with(combinat);
g:=k->sum(stirling2(k,j),j=0..k)^2;
egf:=series((exp(x)-1+log(1+sum(g(k)*x^k/k!,k=1..infinity)))/2,x,20);
seq(n!*coeff(egf,x,n),n=1..20); # Sean A. Irvine, Mar 22 2012

Extensions

More terms from Sean A. Irvine, Mar 21 2012