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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
0, 4, 27, 428, 1375, 15797, 211631, 86540, 1496205, 144045379, 145607407, 3378951221, 17021747431, 51392118293, 214084856611, 13337033800292, 13393340889767, 94103945740529, 3493457389196573, 3503912518228613 (list; graph; refs; listen; history; text; internal format)
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 * A120093 A197987 A133018

Adjacent sequences:  A119027 A119028 A119029 * A119031 A119032 A119033

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Jul 22 2006

STATUS

approved

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Last modified May 15 01:50 EDT 2021. Contains 343909 sequences. (Running on oeis4.)