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A291837 a(n) is the maximal value in row n of triangle A100960.

%I A291837 #9 Sep 05 2017 04:12:56
%S A291837 1,6,100,3525,210861,20545920,2516883516,366723015750,65231311386780,
%T A291837 13434052797314820,3068032280097740670,770387691039763211415,
%U A291837 222066633621598291951425,69102739152239837029025040,23037728813031184811224116360
%N A291837 a(n) is the maximal value in row n of triangle A100960.
%H A291837 Gheorghe Coserea, <a href="/A291837/b291837.txt">Table of n, a(n) for n = 3..126</a>
%H A291837 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.
%F A291837 a(n) ~ k * n^(-4) * r^n * n!, where k=0.000002389700772064... (A291838) and r=26.1841125556... (A291836) (see Bender link).
%o A291837 (PARI)
%o A291837 Q(n,k) = { \\ c-nets with n-edges, k-vertices
%o A291837   if (k < 2+(n+2)\3 || k > 2*n\3, return(0));
%o A291837   sum(i=2, k, sum(j=k, n, (-1)^((i+j+1-k)%2)*binomial(i+j-k,i)*i*(i-1)/2*
%o A291837   (binomial(2*n-2*k+2,k-i)*binomial(2*k-2, n-j) -
%o A291837   4*binomial(2*n-2*k+1, k-i-1)*binomial(2*k-3, n-j-1))));
%o A291837 };
%o A291837 A100960_ser(N) = {
%o A291837 my(x='x+O('x^(3*N+1)), t='t+O('t^(N+4)),
%o A291837    q=t*x*Ser(vector(3*N+1, n, Polrev(vector(min(N+3, 2*n\3), k, Q(n,k)),'t))),
%o A291837    d=serreverse((1+x)/exp(q/(2*t^2*x) + t*x^2/(1+t*x))-1),
%o A291837    g2=intformal(t^2/2*((1+d)/(1+x)-1)));
%o A291837    serlaplace(Ser(vector(N, n, subst(polcoeff(g2, n,'t),'x,'t)))*'x);
%o A291837 };
%o A291837 N=15; apply(p->vecmax(Vecrev(p)), Vec(A100960_ser(N+2)))
%K A291837 nonn
%O A291837 3,2
%A A291837 _Gheorghe Coserea_, Sep 04 2017