A062074 a(n) = n^3 * 3^n.

0, 3, 72, 729, 5184, 30375, 157464, 750141, 3359232, 14348907, 59049000, 235782657, 918330048, 3502727631, 13124466936, 48427561125, 176319369216, 634465620819, 2259436291848, 7971951402153, 27894275208000, 96873331012983, 334145522716632, 1145440056788109, 3904305912313344

Offset: 0

Author

Jason Earls, Jun 27 2001

Keywords

• easy
• nonn

Links

• Harry J. Smith, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81).

Crossrefs

Cf. A000244, A000578.

Programs

Mathematica

Table[n^3 3^n,{n,0,20}] (* or *) LinearRecurrence[{12,-54,108,-81},{0,3,72,729},30] (* Harvey P. Dale, Jun 17 2014 *)

PARI

a(n) = (n^3)*(3^n);

SageMath

[3^n*n^3 for n in (0..30)] # G. C. Greubel, May 10 2022

Formula

G.f.: 3*x*(1+12*x+9*x^2) / (1-3*x)^4. - Colin Barker, Apr 30 2013

a(n) = A000578(n) * A000244(n). - Michel Marcus, Apr 30 2021

E.g.f.: 3*x*(1 + 9*x + 9*x^2)*exp(3*x). - G. C. Greubel, May 10 2022

From Amiram Eldar, Jun 28 2022: (Start)

Sum_{n>=1} 1/a(n) = Li_3(1/3) = 0.3488278611... .

Sum_{n>=1} (-1)^(n+1)/a(n) = -Li_3(-1/3) = 0.3206509480... . (End)