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 A194349 #17 Aug 16 2018 03:08:22
%S A194349 1,2,5,24,129,960,7965,80640,903105,11612160,163451925,2554675200,
%T A194349 43259364225,797058662400,15764670046125,334764638208000,
%U A194349 7571150452490625,182111963185152000,4634731528895593125,124564582818643968000
%N A194349 E.g.f.: -log( sqrt(1-x^2) - x ).
%C A194349 Compare e.g.f. to arccosh(x) = log(sqrt(x^2-1) + x).
%F A194349 a(2*n) = 2^n*(2*n-1)! for n>=1.
%F A194349 a(n) = A100097(n+1)*(n-1)!/2^n for n>=1.
%F A194349 a(n) = (n-1)!/2^n * Sum_{k=0..floor((n+1)/2)} C(n+1,k)*A000129(n+1-2*k) for n >= 1. [From a formula of Paul Barry in A100097]
%F A194349 E.g.f.: log( (sqrt(1-x^2) + x)/(1-2*x^2) ).
%e A194349 E.g.f.: A(x) = x + 2*x^2/2! + 5*x^3/3! + 24*x^4/4! + 129*x^5/5! + ...
%e A194349 where
%e A194349 exp(A(x)) = 1 + 2*(x/2) + 6*(x/2)^2 + 16*(x/2)^3 + 46*(x/2)^4 + 128*(x/2)^5 + ... + A098617(n)*(x/2)^n + ...
%t A194349 With[{nn=30},Rest[CoefficientList[Series[-Log[Sqrt[1-x^2]-x],{x,0,nn}], x] Range[0,nn]!]] (* _Harvey P. Dale_, Dec 01 2011 *)
%o A194349 (PARI) {a(n)=n!*polcoeff(-log(sqrt(1-x^2+x*O(x^n))-x),n)}
%o A194349 (PARI) {A000129(n)=polcoeff(x/(1-2*x-x^2+x*O(x^n)),n)}
%o A194349 {a(n)=if(n<1,0,sum(k=0,floor((n+1)/2),binomial(n+1, k)*A000129(n+1-2*k))*(n-1)!/2^n)}
%Y A194349 Cf. A098617, A100097.
%K A194349 nonn
%O A194349 1,2
%A A194349 _Paul D. Hanna_, Aug 21 2011