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 A002030 Number of connected graphs on n labeled nodes, each node being colored with one of 5 colors, such that no edge joins nodes of the same color. (Formerly M3911 N1606) 3
 1, 5, 20, 300, 9980, 616260, 65814020, 11878194300, 3621432947180, 1880516646144660, 1678121372919602420, 2590609089652498130700, 6947580541943715645962780, 32448510765823652400410879460, 264301377639329321236008592510820 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES R. C. Read, 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 Andrew Howroyd, Table of n, a(n) for n = 0..50 R. C. Read, E. M. Wright, Colored graphs: A correction and extension, Canad. J. Math. 22 1970 594-596. FORMULA E.g.f.: log(B(x)+1) where B(x) = Sum_{n>=0} b(n)x^n/n! and b(n) = Sum_{j=0..n} C(n, j)*2^(j*(n-j)+2)*A000686(j). - Sean A. Irvine, May 27 2013 a(n) = m_n(5) using the functions defined in A002032. - Sean A. Irvine, May 29 2013 MATHEMATICA m = 15; serconv = (CoefficientList[Sum[x^j*2^Binomial[j, 2], {j, 0, m}] + O[x]^m, x]*CoefficientList[(Sum[x^j/(j!*2^Binomial[j, 2]), {j, 0, m}] + O[x]^m)^5, x]) . x^Range[0, m-1]; CoefficientList[1 + Log[serconv] + O[x]^m, x]*Range[0, m-1]! (* Jean-François Alcover, Sep 04 2019, after Andrew Howroyd *) PROG (PARI) seq(n)={Vec(serlaplace(1 + log(serconvol(sum(j=0, n, x^j*2^binomial(j, 2)) + O(x*x^n), (sum(j=0, n, x^j/(j!*2^binomial(j, 2))) + O(x*x^n))^5))))} \\ Andrew Howroyd, Dec 03 2018 CROSSREFS Column k=5 of A322279. Cf. A002032. Sequence in context: A203213 A203206 A032072 * A213148 A202860 A156148 Adjacent sequences:  A002027 A002028 A002029 * A002031 A002032 A002033 KEYWORD nonn AUTHOR EXTENSIONS More terms from Sean A. Irvine, May 27 2013 Name clarified and offset corrected by Andrew Howroyd, Dec 03 2018 STATUS approved

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Last modified October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)