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 A120307 #7 Jun 24 2019 04:14:48 %S A120307 1,3,60,10500,18522000,359400888000,81408613942656000, %T A120307 224737840779305293440000,7812628980363223707442752000000, %U A120307 3508978524227146242839564498172672000000 %N A120307 Inverse determinant of n X n matrix M[i,j] = i*j/(i+j-1). %F A120307 a(n) = 1/Det[ Table[ i*j/(i+j-1), {i, n}, {j, n}]]. a(n+1)/a(n) = A000891[n] = (2n)!(2n+1)! / (n! (n+1)!)^2 = (2n+1)*CatalanNumber[n]^2 = (2n+1)*A000108[n]^2 = C(2n+1,n+1)*CatalanNumber[n] = A001700[n]*A000108[n]. %F A120307 a(n) = A163085(2*n)/(2*n)!. - _Peter Luschny_, Sep 18 2012 %t A120307 Table[ 1/Det[ Table[ i*j/(i+j-1), {i, n}, {j, n}]], {n,1,12}] %o A120307 (Sage) %o A120307 def A120307(n): return A163085(2*n)/factorial(2*n) %o A120307 [A120307(n) for n in (1..10)] # _Peter Luschny_, Sep 18 2012 %Y A120307 Cf. A000108, A000891, A001700. %K A120307 nonn %O A120307 1,2 %A A120307 _Alexander Adamchuk_, Jul 15 2006