A060459 a(n) = (n*(n+1))^3.

0, 8, 216, 1728, 8000, 27000, 74088, 175616, 373248, 729000, 1331000, 2299968, 3796416, 6028568, 9261000, 13824000, 20123648, 28652616, 40001688, 54872000, 74088000, 98611128, 129554216, 168196608, 216000000, 274625000, 345948408, 432081216, 535387328, 658503000

Offset

0,2

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = A002378(n)^3. - Zerinvary Lajos, Apr 11 2006

G.f.: 8*x*(1 + 20*x + 48*x^2 + 20*x^3 + x^4)/(1-x)^7. - Colin Barker, Jan 29 2012

Sum_{n>=1} 1/a(n) = 10 - Pi^2. - Vaclav Kotesovec, Feb 14 2015

Sum_{n>=1} (-1)^(n+1)/a(n) = 3*zeta(3)/2 + 12*log(2) - 10. - Amiram Eldar, Jul 15 2020

E.g.f.: exp(x)*x*(8 + 100*x + 184*x^2 + 98*x^3 + 18*x^4 +x^5). - Stefano Spezia, Jul 01 2024

Example

(0)^3, (1+1)^3, (2+2+2)^3, (3+3+3+3)^3, (4+4+4+4+4)^3, (5+5+5+5+5+5)^3, ...

Maple

seq((n*(n+1))^3, n=0..66);

Mathematica

Table[(n*(n+1))^3, {n, 0, 50}] (* Paolo Xausa, Aug 28 2024 *)

Prog

(PARI) a(n) = { (n*(n + 1))^3 } \\ Harry J. Smith, Jul 05 2009

Crossrefs

Cf. A002378.

Sequence in context: A239222 A275023 A163289 * A007409 A334582 A195506

Adjacent sequences: A060456 A060457 A060458 * A060460 A060461 A060462

Keyword

easy,nonn

Author

Jason Earls, Apr 09 2001

Status

approved