A168526 a(n) = n^6*(n + 1)/2.

0, 1, 96, 1458, 10240, 46875, 163296, 470596, 1179648, 2657205, 5500000, 10629366, 19408896, 33787663, 56471520, 91125000, 142606336, 217238121, 323116128, 470458810, 672000000, 943427331, 1303868896, 1776430668, 2388787200, 3173828125, 4170362976

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A168029.

Programs

Magma

[n^6*(n+1)/2: n in [0..30]]; // Vincenzo Librandi, Jul 25 2016

Mathematica

Table[n^6*(n+1)/2, {n,0,40}] (* G. C. Greubel, Jul 25 2016 *)

SageMath

def A168526(n): return n^5*binomial(n+1,2)
print([A168526(n) for n in range(41)]) # G. C. Greubel, Mar 20 2025

Formula

From R. J. Mathar, Dec 16 2009: (Start)

a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) +56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8).

G.f.: x*(1 + 88*x + 718*x^2 + 1208*x^3 + 473*x^4 + 32*x^5)/(1-x)^8. (End)

E.g.f.: (1/2)*x*(2 + 94*x + 391*x^2 + 415*x^3 + 155*x^4 + 22*x^5 + x^6)*exp(x). - G. C. Greubel, Mar 20 2025