A119785 Numerator of the product of the n-th square pyramidal number and the n-th generalized harmonic number in power 2.

1, 25, 343, 1025, 57959, 488579, 266681, 18321733, 185784679, 21651619, 5507071447, 15632832085, 40799043101, 1187015026009, 6362282386111, 13990468150733, 238357395880861, 167890966963712483, 86364397717734821

Offset

1,2

Comments

p^2 divides a(p-1) for prime p>3. p^2 divides a((p-1)/2) for prime p>3.

Links

Table of n, a(n) for n=1..19.

Formula

a(n) = numerator[Sum[i^2,{i,1,n}] * Sum[1/j^2,{j,1,n}]] = numerator[n(n+1)(2n+1)/6 * Sum[1/j^2,{j,1,n}]] = numerator[A000330(n) * ( A007406(n)/A007407(n) )]. Also a(n) = numerator[Sum[Sum[i^2/j^2, {i, 1, n}], {j, 1, n}]].

Mathematica

Numerator[Table[n(n+1)(2n+1)/6*Sum[1/k^2, {k, 1, n}], {n, 1, 30}]]. Numerator[Table[Sum[Sum[i^2/j^2, {i, 1, n}], {j, 1, n}], {n, 1, 30}]].

Crossrefs

Cf. A000330, A007406, A007407.

Sequence in context: A265930 A265922 A136736 * A067457 A055333 A278557

Adjacent sequences: A119782 A119783 A119784 * A119786 A119787 A119788

Keyword

frac,nonn

Author

Alexander Adamchuk, Jun 25 2006

Status

approved