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 A003515 Number of series-reduced connected labeled graphs with n nodes. (Formerly M4009) 6
 0, 1, 1, 0, 5, 51, 3634, 374119, 73161880, 26545249985, 17904840957826, 22602069719494379, 53938857227326533032, 246107945479472758874483, 2170331943503938546383205218, 37340982087637629911717846092591, 1262915556964772342158139988356979872 (list; graph; refs; listen; history; text; internal format)
 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: A124559 A172403 A022516 * A022501 A134097 A299025 Adjacent sequences:  A003512 A003513 A003514 * A003516 A003517 A003518 KEYWORD nonn AUTHOR EXTENSIONS More terms and a(12) corrected by Sean A. Irvine, Jun 17 2015 STATUS approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)