A001095 a(n) = n + n*(n-1)*(n-2)*(n-3)*(n-4).

0, 1, 2, 3, 4, 125, 726, 2527, 6728, 15129, 30250, 55451, 95052, 154453, 240254, 360375, 524176, 742577, 1028178, 1395379, 1860500, 2441901, 3160102, 4037903, 5100504, 6375625, 7893626, 9687627, 11793628, 14250629, 17100750, 20389351

Offset: 0

Author

N. J. A. Sloane, Ray Wills (rwills(AT)vmprofs.estec.esa.nl)

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Equals A052787(n) + n.

Programs

GAP

List([0..35], n-> n + 120*Binomial(n,5)); # G. C. Greubel, Aug 26 2019

Magma

[n + n*(n-1)*(n-2)*(n-3)*(n-4): n in [0..35]]; // Vincenzo Librandi, Apr 30 2011

Maple

seq(n + 5!*binomial(n,5), n=0..35); # G. C. Greubel, Aug 26 2019

Mathematica

Table[n+Times@@(n-Range[0,4]),{n,0,40}] (* or *)  LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,2,3,4,125},40] (* Harvey P. Dale, Oct 08 2017 *)

PARI

vector(35, n, (n-1) + 5!*binomial(n-1,5)) \\ G. C. Greubel, Aug 26 2019

Sage

[n + 120*binomial(n,5) for n in (0..35)] # G. C. Greubel, Aug 26 2019

Formula

G.f.: x*(1 - 4*x + 6*x^2 - 4*x^3 + 121*x^4)/(1-x)^6. - Colin Barker, Jun 25 2012

From G. C. Greubel, Aug 26 2019: (Start)

a(n) = n + 5!*binomial(n,5).

E.g.f.: x*(1 + x^4)*exp(x). (End)

Extensions

More terms from James Sellers, Sep 19 2000