A120287 Numerator of 1/n^3 + 2/(n-1)^3 + 3/(n-2)^3 +...+ (n-1)/2^3 + n.

1, 17, 355, 7715, 203413, 492527, 49601051, 1823359051, 16684019407, 186004308017, 22757931053507, 298630937704541, 50872538998767329, 51223731720255509, 103063783892301061, 7045407930432340853

Offset

1,2

Comments

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

Numerators of the Eulerian numbers T(-3,k) for k = 0,1..., if T(n,k) is extended to negative n by the recurrence T(n,k) = (k+1)*T(n-1,k) + (n-k)*T(n-1,k-1) (indexed as in A173018). - Michael J. Collins, Oct 10 2024

Links

Table of n, a(n) for n=1..16.

Formula

a(n) = numerator[Sum[Sum[1/i^3,{i,1,k}],{k,1,n}]].

Mathematica

Numerator[Table[Sum[Sum[1/i^3, {i, 1, k}], {k, 1, n}], {n, 1, 25}]]

Crossrefs

Cf. A001008, A007406, A007407, A007408, A007410.

Sequence in context: A194729 A081421 A121824 * A222678 A293691 A365678

Adjacent sequences: A120284 A120285 A120286 * A120288 A120289 A120290

Keyword

frac,nonn

Author

Alexander Adamchuk, Jul 07 2006

Status

approved