A016793 - OEIS

%I #20 May 10 2024 01:53:20

%S 32,3125,32768,161051,537824,1419857,3200000,6436343,11881376,

%T 20511149,33554432,52521875,79235168,115856201,164916224,229345007,

%U 312500000,418195493,550731776,714924299,916132832,1160290625,1453933568,1804229351,2219006624,2706784157,3276800000

%N a(n) = (3*n + 2)^5.

%H Vincenzo Librandi, <a href="/A016793/b016793.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F From _Ilya Gutkovskiy_, Jun 16 2016: (Start)

%F G.f.: (32 + 2933*x + 14498*x^2 + 10678*x^3 + 1018*x^4 + x^5)/(1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). (End)

%F From _Amiram Eldar_, Mar 31 2022: (Start)

%F a(n) = A016789(n)^5.

%F Sum_{n>=0} 1/a(n) = 121*zeta(5)/243 - 2*Pi^5/(729*sqrt(3)). (End)

%t Table[(3n+2)^5,{n,0,100}] (* _Mohammad K. Azarian_, Jun 15 2016 *)

%t LinearRecurrence[{6,-15,20,-15,6,-1},{32,3125,32768,161051,537824,1419857},30] (* _Harvey P. Dale_, May 10 2024 *)

%o (Magma) [(3*n+2)^5 : n in [0..30]]; // _Vincenzo Librandi_, Sep 29 2011

%Y Cf. A016789, A016790, A016791, A016792.

%Y Subsequence of A000584.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_