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

1, 6, 100, 3525, 210861, 20545920, 2516883516, 366723015750, 65231311386780, 13434052797314820, 3068032280097740670, 770387691039763211415, 222066633621598291951425, 69102739152239837029025040, 23037728813031184811224116360

Offset

3,2

Links

Gheorghe Coserea, Table of n, a(n) for n = 3..126

E. A. Bender, Z. Gao and N. C. Wormald, The number of labeled 2-connected planar graphs, Electron. J. Combin., 9 (2002), #R43.

Formula

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

Prog

(PARI)
Q(n, k) = { \\ c-nets with n-edges, k-vertices
  if (k < 2+(n+2)\3 || k > 2*n\3, return(0));
  sum(i=2, k, sum(j=k, n, (-1)^((i+j+1-k)%2)*binomial(i+j-k, i)*i*(i-1)/2*
  (binomial(2*n-2*k+2, k-i)*binomial(2*k-2, n-j) -
  4*binomial(2*n-2*k+1, k-i-1)*binomial(2*k-3, n-j-1))));
};
A100960_ser(N) = {
my(x='x+O('x^(3*N+1)), t='t+O('t^(N+4)),
   q=t*x*Ser(vector(3*N+1, n, Polrev(vector(min(N+3, 2*n\3), k, Q(n, k)), 't))),
   d=serreverse((1+x)/exp(q/(2*t^2*x) + t*x^2/(1+t*x))-1),
   g2=intformal(t^2/2*((1+d)/(1+x)-1)));
   serlaplace(Ser(vector(N, n, subst(polcoeff(g2, n, 't), 'x, 't)))*'x);
};
N=15; apply(p->vecmax(Vecrev(p)), Vec(A100960_ser(N+2)))

Crossrefs

Sequence in context: A278430 A131311 A098721 * A214381 A078629 A012497

Adjacent sequences: A291834 A291835 A291836 * A291838 A291839 A291840

Keyword

nonn

Author

Gheorghe Coserea, Sep 04 2017

Status

approved