A168665 - OEIS

%I #10 Sep 08 2022 08:45:49

%S 0,1,16448,7175547,536879104,15258828125,235092632256,2373781166743,

%T 17592187092992,102945568438809,500000005000000,2088624094451411,

%U 7703510805209088,25592946538419637,77784047831612864

%N a(n) = n^7*(n^8 + 1)/2.

%H Vincenzo Librandi, <a href="/A168665/b168665.txt">Table of n, a(n) for n = 0..10000</a>

%F From _G. C. Greubel_, Jul 29 2016: (Start)

%F G.f.: x*(1 + 16432*x + 6912499*x^2 + 424043552*x^3 + 7520619041*x^4 + 51388499408*x^5 + 155693786091*x^6 + 223769429952*x^7 + 155693786091*x^8 + 51388499408*x^9 + 7520619041*x^10 + 424043552*x^11 + 6912499*x^12 + 16432*x^13 + x^14)/(1 - x)^16.

%F E.g.f.: (1/2)*x*(2 + 16446*x + 2375402*x^2 + 42356300*x^3 + 210767060*x^4 + 420693294*x^5 + 408741334*x^6 + 216627840*x^7 + 67128490*x^8 + 12662650*x^9 + 1479478*x^10 + 106470*x^11 + 4550*x^12 + 105*x^13 + x^14)*exp(x). (End)

%t Table[n^7*(n^8 + 1)/2, {n,0,50}] (* _G. C. Greubel_, Jul 29 2016 *)

%o (Magma) [n^7*(n^8+1)/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 28 2011

%K nonn,easy

%O 0,3

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