A119030 Difference between numerator and denominator of the sum of all matrix elements of n X n Hilbert matrix M(i,j)=1/(i+j-1) (i,j = 1..n), A117731[n] - A117664[n].

0, 4, 27, 428, 1375, 15797, 211631, 86540, 1496205, 144045379, 145607407, 3378951221, 17021747431, 51392118293, 214084856611, 13337033800292, 13393340889767, 94103945740529, 3493457389196573, 3503912518228613

Offset

1,2

Comments

p^3 divides a(p^k) for prime p>2 and integer k>0.

Links

Table of n, a(n) for n=1..20.

Formula

a(n) = Numerator[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}]] - Denominator[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}]]. a(n) = A117731[n] - A117664[n].

Mathematica

Numerator[Table[Sum[Sum[1/(i+j-1), {i, 1, n}], {j, 1, n}], {n, 1, 25}]] - Denominator[Table[Sum[Sum[1/(i+j-1), {i, 1, n}], {j, 1, n}], {n, 1, 25}]]

Crossrefs

Cf. A117731, A117664.

Sequence in context: A271616 A123672 A269869 * A356806 A120093 A197987

Adjacent sequences: A119027 A119028 A119029 * A119031 A119032 A119033

Keyword

nonn

Author

Alexander Adamchuk, Jul 22 2006

Status

approved