OFFSET
0,3
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).
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)
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 *)
PROG
(Magma) [n + n*(n-1)*(n-2)*(n-3): n in [0..35]]; // Vincenzo Librandi, Apr 30 2011
(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
(GAP) List([0..35], n-> n + 24*Binomial(n, 4)); # G. C. Greubel, Aug 26 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Ray Wills (rwills(AT)vmprofs.estec.esa.nl)
EXTENSIONS
More terms from James A. Sellers, Sep 19 2000
STATUS
approved