A133754 a(n) = n^5 - n^3.

0, 0, 24, 216, 960, 3000, 7560, 16464, 32256, 58320, 99000, 159720, 247104, 369096, 535080, 756000, 1044480, 1414944, 1883736, 2469240, 3192000, 4074840, 5142984, 6424176, 7948800, 9750000, 11863800, 14329224, 17188416, 20486760, 24273000, 28599360, 33521664

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = 12*n*(2*binomial(n+2,4)- binomial(n+1,3)). - Gary Detlefs, Mar 25 2012

Sum_{n>=2} 1/a(n) = 5/4 - zeta(3). - Daniel Suteu, Feb 06 2017

From G. C. Greubel, Sep 02 2019: (Start)

G.f.: 24*x^2*(1 + 3*x + x^2)/(1-x)^6.

E.g.f.: x^2*(12 + 24*x + 10*x^2 + x^3)*exp(x). (End)

Sum_{n>=2} (-1)^n/a(n) = 3*zeta(3)/4 + 2*log(2) - 9/4. - Amiram Eldar, Jan 09 2021

Maple

seq(n^5 - n^3, n=0..50); # G. C. Greubel, Sep 02 2019

Mathematica

Table[n^5-n^3, {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)

Prog

(Magma) [n^5-n^3: n in [0..50]]; // Vincenzo Librandi, Feb 20 2012
(PARI) a(n)=n^5-n^3 \\ Charles R Greathouse IV, Feb 20 2012
(Sage) [n^5 - n^3 for n in (0..50)] # G. C. Greubel, Sep 02 2019
(GAP) List([0..50], n-> n^5 - n^3); # G. C. Greubel, Sep 02 2019

Crossrefs

Cf. A000578, A000584, A155977.

Sequence in context: A269496 A221434 A008655 * A104670 A205968 A232474

Adjacent sequences: A133751 A133752 A133753 * A133755 A133756 A133757

Keyword

easy,nonn

Author

Rolf Pleisch, Mar 16 2008

Status

approved