A168299 a(n) = 1 + 3^n * n^3.
1, 4, 73, 730, 5185, 30376, 157465, 750142, 3359233, 14348908, 59049001, 235782658, 918330049, 3502727632, 13124466937, 48427561126, 176319369217, 634465620820, 2259436291849, 7971951402154, 27894275208001, 96873331012984
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Crossrefs
Cf. A024026.
Programs
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Magma
[1+n^3*3^n: n in [0..30]]; // Vincenzo Librandi, Jul 02 2011
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Mathematica
f[n_]:=3^n-n^3; Table[Numerator[f[n]],{n,0,-50,-1}] -
PARI
for(n=0,100,print1(1+(n^3)*(3^n),",")) \\ Edward Jiang, Nov 22 2013
Formula
From R. J. Mathar, Nov 24 2009: (Start)
a(n) = 1 + A062074(n).
G.f.: (1 -9*x +87*x^2 -117*x^3 +54*x^4)/((1-x)*(3*x-1)^4). (End)
E.g.f.: exp(x) + 3*x*(1 + 9*x + 9*x^2)*exp(3*x). - G. C. Greubel, Jul 17 2016
Extensions
Corrected offset, and simplified the definition - R. J. Mathar, Nov 24 2009
Comments