OFFSET
0,2
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).
FORMULA
G.f.: 3*x*(1+12*x+9*x^2) / (1-3*x)^4. - Colin Barker, Apr 30 2013
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)
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 *)
PROG
(PARI) a(n) = (n^3)*(3^n);
(PARI) { for (n=0, 200, write("b062074.txt", n, " ", n^3 * 3^n) ) } \\ Harry J. Smith, Jul 31 2009
(SageMath) [3^n*n^3 for n in (0..30)] # G. C. Greubel, May 10 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jun 27 2001
STATUS
approved