A003515 Number of series-reduced connected labeled graphs with n nodes. (Formerly M4009)

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

Offset

0,5

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.

Formula

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

Prog

(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

Crossrefs

Row sums of A331438.

Column sums of A331437.

Cf. A003514, A331584.

Sequence in context: A348023 A172403 A022516 * A022501 A134097 A299025

Adjacent sequences: A003512 A003513 A003514 * A003516 A003517 A003518

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved