A024002 a(n) = 1 - n^4.

1, 0, -15, -80, -255, -624, -1295, -2400, -4095, -6560, -9999, -14640, -20735, -28560, -38415, -50624, -65535, -83520, -104975, -130320, -159999, -194480, -234255, -279840, -331775, -390624, -456975, -531440, -614655, -707280, -809999, -923520, -1048575, -1185920, -1336335, -1500624

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..630

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = -A123865(n) for n>0.

From G. C. Greubel, May 11 2017: (Start)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: (1 - 5*x - 5*x^2 - 15*x^3)/(1 - x)^5.

E.g.f.: (1 - x - 7*x^2 - 6*x^3 - x^4)*exp(x). (End)

Sum_{k>=2} -1/a(k) = A256919 = 7/8 - Pi*coth(Pi)/4. - Vaclav Kotesovec, Dec 08 2020

Mathematica

Table[1 - n^4, {n, 0, 50}] (* Bruno Berselli, Jun 12 2015 *)
CoefficientList[Series[(1 - 5*x - 5*x^2 - 15*x^3)/(1 - x)^5, {x, 0, 50}], x] (* G. C. Greubel, May 11 2017 *)

Prog

(Magma) [1-n^4: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
(PARI) x='x+O('x^50); Vec((1 - 5*x - 5*x^2 - 15*x^3)/(1 - x)^5) \\ G. C. Greubel, May 11 2017

Crossrefs

Cf. A123865.

Sequence in context: A059377 A370533 A123865 * A050149 A055815 A370535

Adjacent sequences: A023999 A024000 A024001 * A024003 A024004 A024005

Keyword

sign,easy

Author

N. J. A. Sloane

Extensions

Corrected by T. D. Noe, Nov 08 2006

Status

approved