A001096 a(n) = n + n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5).

0, 1, 2, 3, 4, 5, 726, 5047, 20168, 60489, 151210, 332651, 665292, 1235533, 2162174, 3603615, 5765776, 8910737, 13366098, 19535059, 27907220, 39070101, 53721382, 72681863, 96909144, 127512025, 165765626, 213127227, 271252828, 342014429

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Formula

G.f.: x*(1 -5*x +10*x^2 -10*x^3 +5*x^4 +719*x^5)/(1-x)^7. - Ralf Stephan, Dec 30 2002

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

a(n) = n + 6!*binomial(n,6).

E.g.f.: x*(1 + x^5)*exp(x). (End)

Maple

seq(n + 6!*binomial(n, 6), n=0..35); # G. C. Greubel, Aug 26 2019

Mathematica

Table[n + 6!*Binomial[n, 6], {n, 0, 35}] (* G. C. Greubel, Aug 26 2019 *)

Prog

(Magma) [n + n*(n-1)*(n-2)*(n-3)*(n-4)*(n-5): n in [0..35]]; // Vincenzo Librandi, Apr 30 2011
(PARI) vector(35, n, (n-1) + 6!*binomial(n-1, 6)) \\ G. C. Greubel, Aug 26 2019
(Sage) [n + 720*binomial(n, 6) for n in (0..35)] # G. C. Greubel, Aug 26 2019
(GAP) List([0..35], n-> n + 720*Binomial(n, 6)); # G. C. Greubel, Aug 26 2019

Crossrefs

Equals A053625(n) + n.

Cf. A001094, A001095.

Sequence in context: A061340 A004889 A037435 * A004900 A355728 A062937

Adjacent sequences: A001093 A001094 A001095 * A001097 A001098 A001099

Keyword

nonn

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