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 A286757 Number of labeled connected rooted trivalent graphs with 2n nodes. 1
 0, 4, 120, 33600, 18471600, 18386121600, 30231607606200, 76388992266787200, 281063897503929540000, 1444102677105174358272000, 10020068498645397815029407000, 91355440119583548608158042584000, 1069762020017605579789451640683370000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A006607 gives values matching Table 1 (p. 342) of Wormald. However, the values in the table for n > 4 do not appear to match formulas given for generating the table. REFERENCES R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977. LINKS N. C. Wormald, Triangles in labeled cubic graphs, pp. 337-345 of Combinatorial Mathematics (Canberra, 1977), Lect. Notes Math. 686, 1978. FORMULA Let b(0)=b(1)=0, b(n) = 2*binomial(2*n, 2)*b(n-1) + 12*binomial(2*n, 4)*b(n-2) + 6*binomial(2*n, 3)*A002829(n-1) + 60*binomial(2*n, 5)*A002829(n-2) + 1260*binomial(2*n, 7)*A002829(n-3). a(n)=b(n) except a(2)=4. Let Q(x) be an e.g.f. for A002829: Q(x) = 1 + (1/4!)*x^4 + (70/6!)*x^6 + (19355/8!)*x^8 + ...; then A(x), the e.g.f. for this sequence, satisfies (2 - 2*x^2 - x^4) * (A(x) - (1/6)*x^4) = (2*x^3 + x^5 + (1/2)*x^7) * Q'(x) where Q'(x) is the derivative of Q(x) with respect to x. CROSSREFS Cf. A002829, A006607. Sequence in context: A071304 A213957 A006607 * A239187 A062081 A053881 Adjacent sequences:  A286754 A286755 A286756 * A286758 A286759 A286760 KEYWORD nonn AUTHOR Sean A. Irvine, May 13 2017 STATUS approved

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Last modified July 29 09:31 EDT 2021. Contains 346344 sequences. (Running on oeis4.)