A085540 a(n) = n*(n + 1)^3.

0, 8, 54, 192, 500, 1080, 2058, 3584, 5832, 9000, 13310, 19008, 26364, 35672, 47250, 61440, 78608, 99144, 123462, 152000, 185220, 223608, 267674, 317952, 375000, 439400, 511758, 592704, 682892, 783000, 893730, 1015808, 1149984, 1297032, 1457750, 1632960

Offset: 0

Author

N. J. A. Sloane, Jul 05 2003

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A085537 (same sequence with a 0 prepended), A092364.

Programs

Magma

[n*(n+1)^3: n in [0..40]]; // Vincenzo Librandi, Aug 15 2016

Mathematica

Table[n (n + 1)^3, {n, 0, 40}] (* Vincenzo Librandi, Aug 15 2016 *)
LinearRecurrence[{5,-10,10,-5,1},{0,8,54,192,500},40] (* Harvey P. Dale, May 06 2019 *)

Formula

a(n) = 2*A092364(n+1). - Zerinvary Lajos, May 09 2007

G.f.: -2*x*(4 + 7*x + x^2)/(x - 1)^5. - R. J. Mathar, Mar 10 2011

a(n) = A085537(n-1). - Eric W. Weisstein, Sep 08 2017

E.g.f.: exp(x)*x*(8 + 19*x + 9*x^2 + x^3). - Stefano Spezia, Jun 10 2023

From Amiram Eldar, Jul 02 2023: (Start)

Sum_{n>=1} 1/a(n) = 3 - Pi^2/6 - zeta(3).

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/12 + 2*log(2) + 3*zeta(3)/4 - 3. (End)