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 A201732 #11 Feb 17 2025 01:31:42
%S A201732 1,2,18,386,15150,946082,86148762,10776331778,1773210244230,
%T A201732 371367615732002,96462262816769586,30433572793375652738,
%U A201732 11463680237091180885150,5081782052880868302982562,2618864991559576227420716490,1552537179057766207300655437826
%N A201732 a(n) = [x^n/n!] (1/x) * log( (n+1 - n*exp(x)) / (n+2 - (n+1)*exp(x)) ).
%C A201732 The function log((n+1 - n*exp(x))/(n+2 - (n+1)*exp(x))) equals the (n+1)-th iteration of log(1/(2-exp(x))), the e.g.f. of A000629 (with offset 1), where A000629(n) is the number of necklaces of partitions of n+1 labeled beads.
%F A201732 a(n) = A201731(n+1) / (n+1).
%o A201732 (PARI) {a(n)=n!*polcoeff((1/x)*log((n+1 - n*exp(x+O(x^(n+2))))/(n+2 - (n+1)*exp(x+O(x^(n+2))))),n)}
%Y A201732 Cf. A201731, A000629.
%K A201732 nonn
%O A201732 0,2
%A A201732 _Paul D. Hanna_, Dec 04 2011