This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384967 #8 Jun 15 2025 14:37:25
%S A384967 0,0,1,2,7,22,76,271,1001,3765,14381,55450,214880,835663,3255652,
%T A384967 12698352,49559793,193513944,755852101,2953214386,11541989533,
%U A384967 45123241746,176465152051,690340349398,2701579878022,10576116931462,41418132927403,162259989848094,635899817853002,2492993368347594
%N A384967 Number of unsensed simple planar maps with n vertices and 2 faces.
%C A384967 In other words, a(n) is the number of embeddings on the sphere of connected simple unicyclic planar graphs with n nodes.
%o A384967 (PARI)
%o A384967 G1(n)={my(g=(1-sqrt(1-4*x^2 + O(x^(n+2))))/(2*x^2)); ((1 + x/(1-x-x^2*g)^2)^2/(1 - x^2*g^2) - 1)/2 + 1/(1 - x*g) - 1 - x*(g^2/(1 - x*g)^2 + g) - x^2*(g^4/(1 - x*g)^4 + 3*g^2)/2}
%o A384967 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)) - x*(c(1)^2 + c(2)) - x^2*(c(1)^4 + 3*c(2)^2)/2}
%o A384967 seq(n)={Vec(G1(n)+G2(n), -n)/4}
%Y A384967 Column 2 of A384963.
%Y A384967 Also subdiagonal of A379430.
%Y A384967 Cf. A001429, A006081 (cycle is loop), A380239 (not necessarily simple), A384966 (sensed version).
%K A384967 nonn
%O A384967 1,4
%A A384967 _Andrew Howroyd_, Jun 15 2025