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A062074
a(n) = n^3 * 3^n.
12
0, 3, 72, 729, 5184, 30375, 157464, 750141, 3359232, 14348907, 59049000, 235782657, 918330048, 3502727631, 13124466936, 48427561125, 176319369216, 634465620819, 2259436291848, 7971951402153, 27894275208000
OFFSET
0,2
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)
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
Sequence in context: A089537 A321530 A374898 * A290004 A332188 A071645
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jun 27 2001
STATUS
approved