%I #22 Sep 08 2022 08:44:41

%S 64,531441,16777216,148035889,729000000,2565726409,7256313856,

%T 17596287801,38068692544,75418890625,139314069504,243087455521,

%U 404567235136,646990183449,1000000000000,1500730351849,2194972623936,3138428376721,4398046511104,6053445140625

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

%H Vincenzo Librandi, <a href="/A017010/b017010.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 From _Wesley Ivan Hurt_, Apr 22 2016: (Start)

%F G.f.: (64 + 530993*x + 13058473*x^2 + 41753398*x^3 + 26472118*x^4 + 2876609*x^5 + 15625*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).

%F a(n) = A001014(A017005(n)). (End)

%F E.g.f.: (64 + 531377*x + 7857199*x^2 + 16549750*x^3 + 9808085*x^4 + 1966419*x^5 + 117649*x^6)*exp(x). - _Ilya Gutkovskiy_, Apr 23 2016

%p A017010:=n->(7*n+2)^6: seq(A017010(n), n=0..40); # _Wesley Ivan Hurt_, Apr 22 2016

%t (7 Range[0, 30] + 2)^6 (* _Wesley Ivan Hurt_, Apr 22 2016 *)

%o (Magma) [(7*n+2)^6: n in [0..25]]; // _Vincenzo Librandi_, Jul 13 2011

%o (PARI) lista(nn) = for(n=0, nn, print1((7*n+2)^6, ", ")); \\ _Altug Alkan_, Apr 24 2016

%Y Cf. A001014, A017005.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_