A017520 - OEIS

%I #18 Sep 08 2022 08:44:43

%S 1000000000000,7355827511386641,1152921504606846976,

%T 39959630797262576401,614787626176508399616,5688009063105712890625,

%U 37133262473195501387776,188031682201497672618081,784716723734800033386496,2812664781782894485727281

%N a(n) = (11*n + 10)^12.

%H G. C. Greubel, <a href="/A017520/b017520.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

%F From _G. C. Greubel_, Oct 29 2019: (Start)

%F G.f.: (1000000000000 + 7342827511386641*x + 1057373746958820643*x^2 + 25545119783261723711*x^3 + 183137251503172391205*x^4 + 488143704350667868074*x^5 + 528998728358533109886*x^6 + 234662813343627300126*x^7 + 39635845367890711434*x^8 + 2102226021911800565*x^9 + 21798715126193071*x^10 + 8916100448243*x^11 + x^12)/(1-x)^13.

%F E.g.f.: (1000000000000 + 7354827511386641*x + 569105424792036847*x^2 + 6087155460996032566*x^3 + 19243217071043901221*x^4 + 25018123360727376000*x^5 + 15895943833149490132*x^6 + 5437280856006223356*x^7 + 1053961441036472067*x^8 + 117674853236661875*x^9 + 7405264410708505*x^10 + 241373673336906*x^11 + 3138428376721*x^12)*exp(x). (End)

%p seq((11*n+10)^12, n=0..20); # _G. C. Greubel_, Oct 29 2019

%t (11*Range[0,20]+10)^12 (* _Harvey P. Dale_, Oct 14 2012 *)

%o (Maxima) makelist((11*n+10)^12,n,0,30); /* _Martin Ettl_, Oct 21 2012 */

%o (PARI) vector(21, n, (11*n-1)^12) \\ _G. C. Greubel_, Oct 29 2019

%o (Magma) [(11*n+10)^12: n in [0..20]]; // _G. C. Greubel_, Oct 29 2019

%o (Sage) [(11*n+10)^12 for n in (0..20)] # _G. C. Greubel_, Oct 29 2019

%o (GAP) List([0..20], n-> (11*n+10)^12); # _G. C. Greubel_, Oct 29 2019

%Y Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), this sequence (m=12).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_