cp's OEIS Frontend

A380239 Number of unsensed planar maps with n vertices and 2 faces.

%I A380239 #9 Jan 21 2025 21:29:43
%S A380239 1,2,5,13,35,104,315,1021,3407,11814,41893,151688,556432,2063446,
%T A380239 7709381,28977788,109421539,414759097,1577080457,6013019088,
%U A380239 22980514005,88012484058,337717418145,1298113689274,4997561829650,19267942661664,74386901833067,287540841925770
%N A380239 Number of unsensed planar maps with n vertices and 2 faces.
%C A380239 Also by duality the number of unsensed planar maps with n faces and 2 vertices.
%C A380239 The number of edges is n.
%H A380239 Andrew Howroyd, <a href="/A380239/b380239.txt">Table of n, a(n) for n = 1..1000</a>
%F A380239 a(n) = (A380237(n) + A380238(n))/2.
%o A380239 (PARI)
%o A380239 G1(n)={my(g=(1-sqrt(1-4*x^2 + O(x*x^n)))/(2*x^2)); ((1 + x/(1-x-x^2*g)^2)^2/(1 - x^2*g^2) - 1)/2 + 1/(1 - x*g) - 1}
%o A380239 G2(n)={my(c(d)=(1-sqrt(1-4*x^d + O(x*x^(n+d))))/(2*x^d)); sum(k=1, n, my(m=1+k%2); -(log(2 - c(k)) + log(1 - x^k*c(m*k)^(2/m)))*eulerphi(k)/k, O(x*x^n))}
%o A380239 seq(n)={Vec(G1(n)+G2(n))/4}
%Y A380239 Column 2 of A277741.
%Y A380239 Cf. A380237 (sensed), A380238 (achiral).
%K A380239 nonn
%O A380239 1,2
%A A380239 _Andrew Howroyd_, Jan 19 2025