A120306 Numerator of the sum of all matrix elements of n X n matrix M[i,j]=CatalanNumber[i]/CatalanNumber[j], where CatalanNumber[k]=(2k)!/k!/(k+1)!=A000108[k].

1, 9, 68, 1364, 12064, 58303, 4517375, 1142991, 4251679307, 138473652271, 240881487689, 857560784067, 49571162119157, 12805922830496929, 167798784068528807, 365691567246838709, 46160923354240494523

Offset

1,2

Comments

p divides a(p-1) for primes p in A007645.

Links

Table of n, a(n) for n=1..17.

Formula

a(n) = Numerator[Sum[Sum[(2i)!/(i!)^2/(i+1)/((2j)!/(j!)^2/(j+1)),{i,1,n}],{j,1,n}]].

Mathematica

Numerator[Table[Sum[Sum[(2i)!/(i!)^2/(i+1)/((2j)!/(j!)^2/(j+1)), {i, 1, n}], {j, 1, n}], {n, 1, 20}]]

Crossrefs

Cf. A000108, A014138, A007645.

Sequence in context: A327560 A024119 A348590 * A197425 A089379 A193698

Adjacent sequences: A120303 A120304 A120305 * A120307 A120308 A120309

Keyword

frac,nonn

Author

Alexander Adamchuk, Jul 14 2006

Status

approved