%I #9 Sep 05 2017 04:12:56

%S 1,6,100,3525,210861,20545920,2516883516,366723015750,65231311386780,

%T 13434052797314820,3068032280097740670,770387691039763211415,

%U 222066633621598291951425,69102739152239837029025040,23037728813031184811224116360

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

%H Gheorghe Coserea, <a href="/A291837/b291837.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.

%F a(n) ~ k * n^(-4) * r^n * n!, where k=0.000002389700772064... (A291838) and r=26.1841125556... (A291836) (see Bender link).

%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 N=15; apply(p->vecmax(Vecrev(p)), Vec(A100960_ser(N+2)))

%K nonn

%O 3,2

%A _Gheorghe Coserea_, Sep 04 2017