A168635 a(n) = n^7*(n + 1)/2.

0, 1, 192, 4374, 40960, 234375, 979776, 3294172, 9437184, 23914845, 55000000, 116923026, 232906752, 439239619, 790601280, 1366875000, 2281701376, 3693048057, 5816090304, 8938717390, 13440000000, 19811973951, 28685115712, 40857905364, 57330892800

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Sequences of the form n^7*(n^k + 1)/2: A001015 (k=0), this sequence (k=1), A168636 (k=2), A168660 (k=3), A168661 (k=4), A168662 (k=5), A168663 (k=6), A168664 (k=7), A168665 (k=8), A168666 (k=9), A168667 (k=10).

Programs

Magma

[n^7*(n+1)/2: n in [0..25]]; // Vincenzo Librandi, Jul 29 2016

Mathematica

Table[n^7*(n + 1)/2, {n,0,25}] (* G. C. Greubel, Jul 28 2016 *)

PARI

a(n)=n^7*(n+1)/2 \\ Charles R Greathouse IV, Jul 29 2016

SageMath

def A168635(n): return n^6*binomial(n+1,2)
print([A168635(n) for n in range(31)]) # G. C. Greubel, Mar 23 2025

Formula

From G. C. Greubel, Jul 28 2016: (Start)

G.f.: x*(1 + 183*x + 2682*x^2 + 8422*x^3 + 7197*x^4 + 1611*x^5 + 64*x^6)/(1 - x)^9.

E.g.f.: (1/2)*x*(2 + 190*x + 1267*x^2 + 2051*x^3 + 1190*x^4 + 287*x^5 + 29*x^6 + x^7)*exp(x). (End)