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%I #40 Dec 25 2018 22:35:58
%S 1,10,237,10707,774924,78702536,10273189176,1631331753120,
%T 304206135619160,65030138045062272,15659855107404275280,
%U 4191800375194003211360,1234179902360142341550240,396280329098426228719121280,137779269467538258010671193472
%N Number of 2-connected planar graphs on n labeled nodes.
%C Recurrence known, see Bodirsky et al.
%D Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 419.
%H Gheorghe Coserea, <a href="/A096331/b096331.txt">Table of n, a(n) for n = 3..126</a>
%H E. A. Bender, Z. Gao and N. C. Wormald, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v9i1r43">The number of labeled 2-connected planar graphs</a>, Electron. J. Combin., 9 (2002), #R43.
%H M. Bodirsky, C. Groepl and M. Kang, <a href="http://dx.doi.org/10.1007/3-540-45061-0_84">Generating Labeled Planar Graphs Uniformly At Random</a>, ICALP03 Eindhoven, LNCS 2719, Springer Verlag (2003), 1095 - 1107.
%H O. Gimenez and M. Noy, <a href="http://arXiv.org/abs/math.CO/0501269">Asymptotic enumeration and limit laws of planar graphs</a>, arXiv:math/0501269 [math.CO], 2005.
%F a(n) ~ g * n^(-7/2) * r^n * n!, where g=0.00000370445941594... (A291835) and r=26.1841125556... (A291836) (see Bender link). - _Gheorghe Coserea_, Sep 03 2017
%o (PARI)
%o Q(n,k) = { \\ c-nets with n-edges, k-vertices
%o if (k < 2+(n+2)\3 || k > 2*n\3, return(0));
%o sum(i=2, k, sum(j=k, n, (-1)^((i+j+1-k)%2)*binomial(i+j-k,i)*i*(i-1)/2*
%o (binomial(2*n-2*k+2,k-i)*binomial(2*k-2, n-j) -
%o 4*binomial(2*n-2*k+1, k-i-1)*binomial(2*k-3, n-j-1))));
%o };
%o A100960_ser(N) = {
%o my(x='x+O('x^(3*N+1)), t='t+O('t^(N+4)),
%o q=t*x*Ser(vector(3*N+1, n, Polrev(vector(min(N+3, 2*n\3), k, Q(n,k)),'t))),
%o d=serreverse((1+x)/exp(q/(2*t^2*x) + t*x^2/(1+t*x))-1),
%o g2=intformal(t^2/2*((1+d)/(1+x)-1)));
%o serlaplace(Ser(vector(N, n, subst(polcoeff(g2, n,'t),'x,'t)))*'x);
%o };
%o Vec(subst(A100960_ser(20),'t,1)) \\ _Gheorghe Coserea_, Aug 10 2017
%Y Cf. A066537. Row sums of A100960.
%K nonn
%O 3,2
%A _Steven Finch_, Aug 02 2004
%E More terms from _Gheorghe Coserea_, Aug 05 2017
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