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%I #27 Mar 29 2022 02:59:32
%S 1,4096,117649,1000000,4826809,16777216,47045881,113379904,244140625,
%T 481890304,887503681,1544804416,2565726409,4096000000,6321363049,
%U 9474296896,13841287201,19770609664,27680640625,38068692544,51520374361,68719476736,90458382169,117649000000
%N a(n) = (3*n+1)^6.
%H Vincenzo Librandi, <a href="/A016782/b016782.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = A001014(A016777(n)). - _Michel Marcus_, Jun 15 2016
%F From _Ilya Gutkovskiy_, Jun 15 2016: (Start)
%F G.f.: (1 + 4089*x + 88998*x^2 + 262438*x^3 + 154113*x^4 + 15177*x^5 + 64*x^6)/(1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). (End)
%F Sum_{n>=0} 1/a(n) = PolyGamma(5, 1/3)/87480. - _Amiram Eldar_, Mar 29 2022
%t Table[(3n+1)^6,{n,0,100}] (* _Mohammad K. Azarian_, Jun 15 2016 *)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,4096,117649,1000000,4826809,16777216,47045881},20] (* _Harvey P. Dale_, Sep 30 2016 *)
%o (Magma) [(3*n+1)^6: n in [0..30]]; // _Vincenzo Librandi_, Sep 21 2011
%Y Cf. A001014, A016777, A016778, A016779, A016780, A016781.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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