A168432 - OEIS

%I #18 Mar 20 2025 04:22:16

%S 0,1,2064,265842,8389120,122071875,1088395056,6920652004,34359754752,

%T 141214797765,500000050000,1569214268886,4458050348544,11649042746887,

%U 28346956456560,64873169325000,140737488879616,291311119324809

%N a(n) = n^5*(n^7 + 1)/2.

%H Vincenzo Librandi, <a href="/A168432/b168432.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

%F G.f.: x*(1 + 2051*x + 239088*x^2 + 5093880*x^3 + 33159402*x^4 + 81255702*x^5 + 81256584*x^6 + 33159072*x^7 + 5093805*x^8 + 239183*x^9 + 2032*x^10)/(1-x)^13. - _Vincenzo Librandi_, Jul 23 2016

%F E.g.f.: (1/2)*x*(2 + 2062*x + 86551*x^2 + 611511*x^3 + 1379401*x^4 + 1323652*x^5 + 627396*x^6 + 159027*x^7 + 22275*x^8 + 1705*x^9 + 66*x^10 + x^11)*exp(x). - _G. C. Greubel_, Mar 20 2025

%t Table[n^5*(n^7 + 1)/2, {n,0,30}] (* _G. C. Greubel_, Jul 22 2016 *)

%t CoefficientList[Series[x (1 +2051 x +239088 x^2 +5093880 x^3 +33159402 x^4 + 81255702 x^5 +81256584 x^6 +33159072 x^7 +5093805 x^8 +239183 x^9 +2032 x^10)/(1-x)^13, {x,0,30}], x] (* _Vincenzo Librandi_, Jul 23 2016 *)

%o (Magma) [n^5*(n^7+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 29 2011

%o (SageMath)

%o def A168432(n): return n^5*(n^7+1)//2

%o print(A168432(n) for n in range(31)) # _G. C. Greubel_, Mar 20 2025

%Y Cf. A168351.

%K nonn,easy

%O 0,3

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