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

0,2

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Mathematica

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

Prog

(Magma) [1+n^3*3^n: n in [0..30]]; // Vincenzo Librandi, Jul 02 2011
(PARI) for(n=0, 100, print1(1+(n^3)*(3^n), ", ")) \\ Edward Jiang, Nov 22 2013

Crossrefs

Cf. A024026.

Sequence in context: A327112 A284673 A055556 * A089665 A092871 A222767

Adjacent sequences: A168296 A168297 A168298 * A168300 A168301 A168302

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Nov 22 2009

Extensions

Corrected offset, and simplified the definition - R. J. Mathar, Nov 24 2009

Status

approved