This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A286757 #11 Jan 04 2021 23:04:05 %S A286757 0,4,120,33600,18471600,18386121600,30231607606200,76388992266787200, %T A286757 281063897503929540000,1444102677105174358272000, %U A286757 10020068498645397815029407000,91355440119583548608158042584000,1069762020017605579789451640683370000 %N A286757 Number of labeled connected rooted trivalent graphs with 2n nodes. %C A286757 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. %D A286757 R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977. %H A286757 N. C. Wormald, <a href="http://dx.doi.org/10.1007/BFb0062550">Triangles in labeled cubic graphs</a>, pp. 337-345 of Combinatorial Mathematics (Canberra, 1977), Lect. Notes Math. 686, 1978. %F A286757 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. %F A286757 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. %Y A286757 Cf. A002829, A006607. %K A286757 nonn %O A286757 1,2 %A A286757 _Sean A. Irvine_, May 13 2017