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

1, 3, 18, 131, 1180, 12570, 154525, 2150748, 33399546, 571979428, 10699844995, 216921707622, 4734437392728, 110613829184421, 2752971531611715, 72676980383698345, 2027560176161932735, 59579981648921326791, 1838669555339295257097, 59435431024069408426431

Offset: 3

Author

Gheorghe Coserea, Sep 10 2017

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 3..123
• E. A. Bender, Z. Gao and N. C. Wormald, The number of labeled 2-connected planar graphs, Electron. J. Combin., 9 (2002), #R43.

Crossrefs

Cf. A096331, A290326.

Column sums of A100960.

Programs

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))));
};
seq(N) = {
my(x='x+O('x^(N+3)), t='t,
   q=t*x*Ser(vector(N, n, Polrev(vector(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)), e2=apply(serlaplace, g2));
   Vec(subst(e2, 't, 1));
};
seq(22)