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a(n) = (6n+2)^7.
6

%I #24 Mar 29 2022 02:54:24

%S 128,2097152,105413504,1280000000,8031810176,34359738368,114415582592,

%T 319277809664,781250000000,1727094849536,3521614606208,6722988818432,

%U 12151280273024,20971520000000,34792782221696,55784660123648,86812553324672,131593177923584,194871710000000

%N a(n) = (6n+2)^7.

%H Vincenzo Librandi, <a href="/A016939/b016939.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F a(n) = 128*A016783(n). - _R. J. Mathar_, May 07 2008

%F G.f.: 128*(1 + 16376*x + 692499*x^2 + 3870352*x^3 + 4890287*x^4 + 1475736*x^5 + 77101*x^6 + 128*x^7)/(1 - x)^8. - _Ilya Gutkovskiy_, Jun 16 2016

%F From _Amiram Eldar_, Mar 29 2022: (Start)

%F a(n) = A016933(n)^7.

%F Sum_{n>=0} 1/a(n) = 7*Pi^7/(3149280*sqrt(3)) + 1093*zeta(7)/279936. (End)

%t Table[(6n+2)^7,{n,0,100}] (* _Mohammad K. Azarian_, Jun 15 2016 *)

%o (Magma) [(6*n+2)^7: n in [0..30]]; // _Vincenzo Librandi_, May 04 2011

%Y Cf. A016783, A016933, A016934, A016935, A016936, A016937, A016938.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.