A168371 a(n) = n^5*(n^3 + 1)/2.

0, 1, 144, 3402, 33280, 196875, 843696, 2890804, 8404992, 21552885, 50050000, 107259966, 215115264, 408051007, 738163440, 1281825000, 2148007936, 3488588649, 5510925072, 8493019570, 12801600000, 18913471731, 27440513584

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Programs

Magma

[n^5*(n^3+1)/2: n in [0..30]]; // Vincenzo Librandi, Aug 28 2011

Mathematica

Table[n^5*(n^3 + 1)/2,{n,0,50}] (* G. C. Greubel, Jul 19 2016 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,1,144,3402,33280,196875,843696,2890804,8404992},30] (* Harvey P. Dale, Apr 02 2017 *)

PARI

a(n) = n^5*(n^3+1)/2 \\ Felix Fröhlich, Jul 19 2016

Formula

From G. C. Greubel, Jul 19 2016: (Start)

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).

G.f.: x*(1 + 135*x + 2142*x^2 + 7762*x^3 + 7857*x^4 + 2151*x^5 + 112*x^6)/(1 - x)^9. (End)