A003515 Number of series-reduced connected labeled graphs with n nodes.

0, 1, 1, 0, 5, 51, 3634, 374119, 73161880, 26545249985, 17904840957826, 22602069719494379, 53938857227326533032, 246107945479472758874483, 2170331943503938546383205218, 37340982087637629911717846092591, 1262915556964772342158139988356979872

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Jackson and Reilly paper has typographical error in value for a(12). - Sean A. Irvine, Jun 17 2015

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50 (terms 0..34 from Sean A. Irvine)
• D. M. Jackson and J. W. Reilly, The enumeration of homeomorphically irreducible labeled graphs, J. Combin. Theory, B 19 (1975), 272-286.

Crossrefs

Row sums of A331438.

Column sums of A331437.

Cf. A003514, A331584.

Programs

PARI

\\ See Jackson & Reilly for e.g.f.
seq(n)={my(A=O(x*x^n)); Vec(serlaplace(log((exp(x/2 - x^2/4 + A)/sqrt(1 + x + A))*sum(k=0, n, (2*exp(-x/(1+x) + A))^binomial(k,2) * (x*exp((x^2 + A)/(2*(1 + x))))^k / k!))), -(n+1))} \\ Andrew Howroyd, Jan 24 2020

Formula

E.g.f.: log(B(x)) where B(x) is the e.g.f. for A003514. - Sean A. Irvine, Jun 17 2015

Extensions

More terms and a(12) corrected by Sean A. Irvine, Jun 17 2015