A167543 a(n) = (n-5)*(n-6)*(n-7)*(n-16)/24.

-2, -7, -15, -25, -35, -42, -42, -30, 0, 55, 143, 273, 455, 700, 1020, 1428, 1938, 2565, 3325, 4235, 5313, 6578, 8050, 9750, 11700, 13923, 16443, 19285, 22475, 26040, 30008, 34408, 39270, 44625, 50505, 56943, 63973, 71630, 79950, 88970, 98728, 109263, 120615

Offset

8,1

Links

G. C. Greubel, Table of n, a(n) for n = 8..1000

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

Formula

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

G.f.: x^8*(-2+3*x)/(1-x)^5.

E.g.f.: (1/24)*( -3360 - 1800*x - 420*x^2 - 52*x^3 - 3*x^4 + (3360 - 1560*x + 300*x^2 - 28*x^3 + x^4)*exp(x) ). - G. C. Greubel, Jul 30 2022

Mathematica

Table[(n-5)*(n-6)*(n-7)*(n-16)/24, {n, 8, 60}] (* G. C. Greubel, Jun 15 2016 *)

Prog

(Magma) [Binomial(n-5, 3)*(n-16)/4: n in [8..60]]; // G. C. Greubel, Jul 30 2022
(SageMath) [binomial(n-5, 3)*(n-16)/4 for n in (8..60)] # G. C. Greubel, Jul 30 2022

Crossrefs

Cf. A111373, A135929, A137276.

Sequence in context: A132746 A252475 A350043 * A332495 A184976 A194140

Adjacent sequences: A167540 A167541 A167542 * A167544 A167545 A167546

Keyword

sign,easy

Author

Jamel Ghanouchi, Nov 06 2009

Extensions

Definition simplified, sequence extended by R. J. Mathar, Nov 12 2009

Status

approved