A001094 a(n) = n + n*(n-1)*(n-2)*(n-3).

0, 1, 2, 3, 28, 125, 366, 847, 1688, 3033, 5050, 7931, 11892, 17173, 24038, 32775, 43696, 57137, 73458, 93043, 116300, 143661, 175582, 212543, 255048, 303625, 358826, 421227, 491428, 570053, 657750, 755191, 863072, 982113, 1113058

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 (5,-10,10,-5,1).

Crossrefs

Cf. A001095, A001096, A052762.

Programs

GAP

List([0..35], n-> n + 24*Binomial(n,4)); # G. C. Greubel, Aug 26 2019

Magma

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

Maple

seq(n + 4!*binomial(n,4), n=0..35); # G. C. Greubel, Aug 26 2019

Mathematica

Table[n+n(n-1)(n-2)(n-3),{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{0,1,2,3,28},40] (* Harvey P. Dale, Feb 02 2012 *)

PARI

vector(35, n, (n-1) + 4!*binomial(n-1,4)) \\ G. C. Greubel, Aug 26 2019

Sage

[n + 24*binomial(n,4) for n in (0..35)] # G. C. Greubel, Aug 26 2019

Formula

G.f.: x*(1 -3*x +3*x^2 +23*x^3)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=28. - Harvey P. Dale, Feb 02 2012

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

a(n) = n + 4!*binomial(n,4).

E.g.f.: x*(1+x^3)*exp(x). (End)

Extensions

More terms from James Sellers, Sep 19 2000