A120307 Inverse determinant of n X n matrix M[i,j] = i*j/(i+j-1).

1, 3, 60, 10500, 18522000, 359400888000, 81408613942656000, 224737840779305293440000, 7812628980363223707442752000000, 3508978524227146242839564498172672000000

Offset: 1

Author

Alexander Adamchuk, Jul 15 2006

Keywords

• nonn

Crossrefs

Cf. A000108, A000891, A001700.

Programs

Mathematica

Table[ 1/Det[ Table[ i*j/(i+j-1), {i, n}, {j, n}]], {n,1,12}]

Sage

def A120307(n): return A163085(2*n)/factorial(2*n)
[A120307(n) for n in (1..10)] # Peter Luschny, Sep 18 2012

Formula

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].

a(n) = A163085(2*n)/(2*n)!. - Peter Luschny, Sep 18 2012