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A017199
a(n) = (9*n + 3)^3.
1
27, 1728, 9261, 27000, 59319, 110592, 185193, 287496, 421875, 592704, 804357, 1061208, 1367631, 1728000, 2146689, 2628072, 3176523, 3796416, 4492125, 5268024, 6128487, 7077888, 8120601, 9261000, 10503459, 11852352, 13312053, 14886936, 16581375, 18399744, 20346417
OFFSET
0,1
FORMULA
G.f.: 27*(1 + 60*x + 93*x^2 + 8*x^3)/ (x-1)^4. - R. J. Mathar, Aug 01 2014
a(n) = 27*A016779(n). - R. J. Mathar, Aug 01 2014
From Amiram Eldar, Oct 03 2024: (Start)
a(n) = A017197(n)^3.
Sum_{n>=0} 1/a(n) = 2*Pi^3/(2187*sqrt(3)) + 13*zeta(3)/729. (End)
MATHEMATICA
(9Range[0, 30]+3)^3 (* or *) LinearRecurrence[{4, -6, 4, -1}, {27, 1728, 9261, 27000}, 30] (* Harvey P. Dale, Jun 20 2024 *)
PROG
(Magma) [(9*n+3)^3: n in [0..30]]; // Vincenzo Librandi, Jul 23 2011
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved