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A291841 a(n) is the number of labeled 2-connected planar graphs with n edges.

%I A291841 #9 Sep 10 2017 05:56:12
%S A291841 1,3,18,131,1180,12570,154525,2150748,33399546,571979428,10699844995,
%T A291841 216921707622,4734437392728,110613829184421,2752971531611715,
%U A291841 72676980383698345,2027560176161932735,59579981648921326791,1838669555339295257097,59435431024069408426431
%N A291841 a(n) is the number of labeled 2-connected planar graphs with n edges.
%H A291841 Gheorghe Coserea, <a href="/A291841/b291841.txt">Table of n, a(n) for n = 3..123</a>
%H A291841 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.
%o A291841 (PARI)
%o A291841 Q(n,k) = { \\ c-nets with n-edges, k-vertices
%o A291841   if (k < 2+(n+2)\3 || k > 2*n\3, return(0));
%o A291841   sum(i=2, k, sum(j=k, n, (-1)^((i+j+1-k)%2)*binomial(i+j-k,i)*i*(i-1)/2*
%o A291841   (binomial(2*n-2*k+2,k-i)*binomial(2*k-2, n-j) -
%o A291841   4*binomial(2*n-2*k+1, k-i-1)*binomial(2*k-3, n-j-1))));
%o A291841 };
%o A291841 seq(N) = {
%o A291841 my(x='x+O('x^(N+3)), t='t,
%o A291841    q=t*x*Ser(vector(N, n, Polrev(vector(2*n\3, k, Q(n,k)),t))),
%o A291841    d=serreverse((1+x)/exp(q/(2*t^2*x) + t*x^2/(1+t*x))-1),
%o A291841    g2=intformal(t^2/2*((1+d)/(1+x)-1)), e2=apply(serlaplace, g2));
%o A291841    Vec(subst(e2, 't, 1));
%o A291841 };
%o A291841 seq(22)
%Y A291841 Cf. A096331, A290326.
%Y A291841 Column sums of A100960.
%K A291841 nonn
%O A291841 3,2
%A A291841 _Gheorghe Coserea_, Sep 10 2017