A168299 - OEIS

%I #21 Sep 08 2022 08:45:49

%S 1,4,73,730,5185,30376,157465,750142,3359233,14348908,59049001,

%T 235782658,918330049,3502727632,13124466937,48427561126,176319369217,

%U 634465620820,2259436291849,7971951402154,27894275208001,96873331012984

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

%C Numerator of 3^(-n) + n^3.

%H Vincenzo Librandi, <a href="/A168299/b168299.txt">Table of n, a(n) for n = 0..1000</a>

%F From _R. J. Mathar_, Nov 24 2009: (Start)

%F a(n) = 1 + A062074(n).

%F G.f.: (1 -9*x +87*x^2 -117*x^3 +54*x^4)/((1-x)*(3*x-1)^4). (End)

%F E.g.f.: exp(x) + 3*x*(1 + 9*x + 9*x^2)*exp(3*x). - _G. C. Greubel_, Jul 17 2016

%t f[n_]:=3^n-n^3; Table[Numerator[f[n]],{n,0,-50,-1}]

%o (Magma) [1+n^3*3^n: n in [0..30]]; // _Vincenzo Librandi_, Jul 02 2011

%o (PARI) for(n=0,100,print1(1+(n^3)*(3^n),",")) \\ _Edward Jiang_, Nov 22 2013

%Y Cf. A024026.

%K nonn,easy

%O 0,2

%A _Vladimir Joseph Stephan Orlovsky_, Nov 22 2009

%E Corrected offset, and simplified the definition - _R. J. Mathar_, Nov 24 2009