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 A246599 Number of connected trivalent bipartite labeled graphs with 2n labeled nodes. 2
 10, 840, 257040, 137214000, 118248530400, 154686980448000, 292276881344448000, 766864651478365440000, 2706292794907249067520000, 12512021073989410699165440000, 74128448237031250090060032000000, 552320243355746711191770103680000000, 5092467146398443040845772685937408000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS R. C. Read incorrectly has a(7) = 118237555800 and a(8) = 154652926428000 which he calculated by hand. REFERENCES R. C. Read, Some Enumeration Problems in Graph Theory. Ph.D. Dissertation, Department of Mathematics, Univ. London, 1958. LINKS Andrew Howroyd, Table of n, a(n) for n = 3..50 R. C. Read, Letter to N. J. A. Sloane, Feb 04 1971 (gives initial terms of this sequence) FORMULA a(n) = binomial(2*n-1, n)*A001501(n) - Sum_{k=1..n-1} binomial(2*n-1, 2*k) * binomial(2*k, k) * A001501(k) * a(n-k). - Andrew Howroyd, May 22 2018 MATHEMATICA b[n_] := n!^2*Sum[2^(2k-n) 3^(k-n)(3(n-k))!*HypergeometricPFQ[{k-n, k-n}, {3(k-n)/2, 1/2 + 3(k-n)/2}, -9/2]/(k! (n-k )!^2), {k, 0, n}]/6^n; a[n_] := a[n] = Binomial[2n-1, n] b[n] - Sum[Binomial[2n-1, 2k] Binomial[2 k, k] b[k] a[n-k], {k, 1, n-1}]; Table[a[n], {n, 3, 20}] (* Jean-François Alcover, Jul 07 2018, after Andrew Howroyd *) PROG (PARI) \\ here b(n) is A001501 b(n) = {n!^2 * sum(j=0, n, sum(i=0, n-j, my(k=n-i-j); (j + 3*k)! / (3^i * 36^k * i! * k!^2)) / (j! * (-2)^j))} seq(n)={my(v=vector(n, n, b(n)*binomial(2*n, n)), u=vector(n)); for(n=1, #u, u[n]=v[n] - sum(k=3, n-3, binomial(2*n-1, 2*k)*v[k]*u[n-k])); u[3..n]/2} \\ Andrew Howroyd, May 22 2018 CROSSREFS Cf. A001501, A002829, A004109, A006714. Sequence in context: A013434 A013436 A013437 * A006714 A203533 A015033 Adjacent sequences:  A246596 A246597 A246598 * A246600 A246601 A246602 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 08 2014 EXTENSIONS a(7)-a(8) corrected and a(9)-a(12) computed with nauty by Sean A. Irvine, Jun 27 2017 Terms a(13) and beyond from Andrew Howroyd, May 22 2018 STATUS approved

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Last modified January 21 13:55 EST 2020. Contains 331113 sequences. (Running on oeis4.)