A168412 - OEIS

%I #16 Sep 08 2022 08:45:49

%S 0,1,1040,88695,2097664,24415625,181402416,988671775,4294983680,

%T 15690559329,50000050000,142655915831,371504309760,896080382665,

%U 2024782853744,4324878309375,8796093546496,17135948863745

%N a(n) = n^5*(n^6 + 1)/2.

%H Vincenzo Librandi, <a href="/A168412/b168412.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

%F G.f.: x*(1 + 1028*x + 76281*x^2 + 1101744*x^3 + 4869222*x^4 + 7861848*x^5 + 4869222*x^6 + 1101744*x^7 + 76281*x^8 + 1028*x^9 + x^10)/(1-x)^12. - _Vincenzo Librandi_, Jul 23 2016

%F a(n) = 12*a(n-1)-66*a(n-2)+220*a(n-3)-495*a(n-4)+792*a(n-5)-924*a(n-6)+792*a(n-7)-495*a(n-8)+220*a(n-9)-66*a(n-10)+12*a(n-11)-a(n-12). - _Wesley Ivan Hurt_, Oct 02 2021

%t Table[n^5*(n^6 + 1)/2, {n, 0, 25}] (* _G. C. Greubel_, Jul 22 2016 *)

%t CoefficientList[Series[x  (1 + 1028 x + 76281 x^2 + 1101744 x^3 + 4869222 x^4 + 7861848 x^5 + 4869222 x^6 + 1101744 x^7 + 76281 x^8 + 1028 x^9 + x^10)/(1 - x)^12, {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 23 2016 *)

%o (Magma) [n^5*(n^6+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 29 2011

%K nonn,easy

%O 0,3

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