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a(n) = (11*n + 7)^7.
12

%I #19 Sep 08 2022 08:44:42

%S 823543,612220032,17249876309,163840000000,897410677851,3521614606208,

%T 11047398519097,29509034655744,69833729609375,150363025899136,

%U 300124211606973,562949953421312,1002544368429379,1708593750000000,2804020163098721,4453476124377088,6873178582377927

%N a(n) = (11*n + 7)^7.

%H Vincenzo Librandi, <a href="/A017479/b017479.txt">Table of n, a(n) for n = 0..10000</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 From _G. C. Greubel_, Sep 19 2019: (Start)

%F G.f.: (823543 +605631688*x +12375175257*x^2 +42937032016*x^3 +35460540721 *x^4 +6665393928*x^5 +170728303*x^6 +16384*x^7)/(1-x)^8.

%F E.g.f.: (823543 +611396489*x +8013129894*x^2 +18987701271*x^3 + 14295911630*x^4 +4196022754*x^5 +496037080*x^6 +19487171*x^7)*exp(x). (End)

%p seq((11*n+7)^7, n=0..20); # _G. C. Greubel_, Sep 19 2019

%t (11Range[0,20]+7)^7 (* _Harvey P. Dale_, Mar 24 2011 *)

%o (Magma) [(11*n+7)^7: n in [0..20]]; // _Vincenzo Librandi_, Sep 04 2011

%o (PARI) vector(20, n, (11*n-4)^7) \\ _G. C. Greubel_, Sep 19 2019

%o (Sage) [(11*n+7)^7 for n in (0..20)] # _G. C. Greubel_, Sep 19 2019

%o (GAP) List([0..20], n-> (11*n+7)^7); # _G. C. Greubel_, Sep 19 2019

%Y Powers of the form (11*n+7)^m: A017473 (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), this sequence (m=7), A017480 (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_