A168371 - OEIS

%I #17 Sep 08 2022 08:45:49

%S 0,1,144,3402,33280,196875,843696,2890804,8404992,21552885,50050000,

%T 107259966,215115264,408051007,738163440,1281825000,2148007936,

%U 3488588649,5510925072,8493019570,12801600000,18913471731,27440513584

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

%H Vincenzo Librandi, <a href="/A168371/b168371.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

%F From _G. C. Greubel_, Jul 19 2016: (Start)

%F 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).

%F 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)

%t Table[n^5*(n^3 + 1)/2,{n,0,50}] (* _G. C. Greubel_, Jul 19 2016 *)

%t 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 *)

%o (Magma) [n^5*(n^3+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 28 2011

%o (PARI) a(n) = n^5*(n^3+1)/2 \\ _Felix Fröhlich_, Jul 19 2016

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Dec 11 2009