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%I #79 Jan 26 2024 04:42:16
%S 1,27,125,343,729,1331,2197,3375,4913,6859,9261,12167,15625,19683,
%T 24389,29791,35937,42875,50653,59319,68921,79507,91125,103823,117649,
%U 132651,148877,166375,185193,205379,226981,250047,274625,300763,328509,357911,389017,421875
%N Odd cubes: a(n) = (2*n + 1)^3.
%C Partial sums of A010014. - _Jani Melik_, May 20 2013
%C Terms end in the repeating sequence 1, 7, 5, 3, 9, ... - _Melvin Peralta_, Jul 08 2015
%D Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3.
%H Vincenzo Librandi, <a href="/A016755/b016755.txt">Table of n, a(n) for n = 0..10000</a>
%H Marc Chamberland and Armin Straub, <a href="https://doi.org/10.1016/j.aam.2013.07.003">On gamma quotients and infinite products</a>, Advances in Applied Mathematics, Vol. 51, No. 5 (2013), pp. 546-562.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F Sum_{n >= 0} 1/a(n) = 7 * zeta(3) / 8.
%F G.f.: (1+23*x+23*x^2+x^3)/(1-4*x+6*x^2-4*x^3+x^4). - _Colin Barker_, Jan 02 2012
%F a(n) = A000578(A005408(n)). - _Michel Marcus_, Jul 09 2015
%F E.g.f.: exp(x)*(1 + 26*x + 36*x^2 + 8*x^3). See A154537, row n=3. - _Wolfdieter Lang_, Mar 12 2017
%F From _Bruce J. Nicholson_, Dec 08 2019: (Start)
%F a(n) = 24 * A000330(n) + A005408(n).
%F a(n) = 2 * A005917(n+1) - A005408(n). (End)
%F Sum_{n>=0} (-1)^n/a(n) = Pi^3/32 (A153071). - _Amiram Eldar_, Oct 10 2020
%F Product_{n>=1} (1 - (-1)^n/a(n)) = (Pi/12)*(1 + sqrt(2)*cosh(sqrt(3)*Pi/4)) (Chamberland and Straub, 2013). - _Amiram Eldar_, Jan 26 2024
%t Range[1,101,2]^3 (* _Harvey P. Dale_, Nov 18 2013 *)
%o (Magma) [(2*n+1)^3: n in [0..50]]; // _Vincenzo Librandi_, Sep 05 2011
%o (PARI) a(n)=(2*n+1)^3 \\ _Charles R Greathouse IV_, Jan 02 2012
%o (Python)
%o def a(n): return (2*n+1)**3
%o print([a(n) for n in range(38)]) # _Michael S. Branicky_, Jan 27 2021
%Y Cf. A000578, A005408, A010014, A016743, A153071, A154537.
%Y Cf. A000330, A005917, A069074.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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