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
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).
Programs
-
Magma
[Binomial(n-5,3)*(n-16)/4: n in [8..60]]; // 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 *) -
SageMath
[binomial(n-5,3)*(n-16)/4 for n in (8..60)] # G. C. Greubel, Jul 30 2022
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
Extensions
Definition simplified, sequence extended by R. J. Mathar, Nov 12 2009