A017494 - OEIS

%I #13 Sep 08 2022 08:44:42

%S 1073741824,6131066257801,590490000000000,13422659310152401,

%T 144555105949057024,984930291881790849,4923990397355877376,

%U 19687440434072265625,66483263599150104576,196715135728956532249,523383555379856794624,1276136419117121619201,2892546549760000000000

%N a(n) = (11*n + 8)^10.

%H G. C. Greubel, <a href="/A017494/b017494.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F From _G. C. Greubel_, Sep 22 2019: (Start)

%F G.f.: (1073741824 +6119255097737*x +523107326964509*x^2 +7264300786930496 *x^3 +28371531939645368*x^4 +37662294296897282*x^5 +17578871136786818* x^6 +2623025688296696*x^7 +92185633683584*x^8 +289254005437*x^9 +59049* x^10)/(1-x)^11.

%F E.g.f.: (1073741824 +6129992515977*x +289114470613111*x^2 +1944930239197330*x^3 +3932620229881585*x^4 +3254225912463141*x^5 + 1282086963575187*x^6 +258144995263320*x^7 +26861311378110*x^8 + 1355819922325*x^9 +25937424601*x^10)*exp(x). (End)

%p seq((11*n+8)^10, n=0..20); # _G. C. Greubel_, Sep 22 2019

%t (11*Range[21] -3)^10 (* _G. C. Greubel_, Sep 22 2019 *)

%t LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1073741824,6131066257801,590490000000000,13422659310152401,144555105949057024,984930291881790849,4923990397355877376,19687440434072265625,66483263599150104576,196715135728956532249,523383555379856794624},20] (* _Harvey P. Dale_, May 08 2022 *)

%o (PARI) vector(20, n, (11*n-3)^10) \\ _G. C. Greubel_, Sep 22 2019

%o (Magma) [(11*n+8)^10: n in [0..20]]; // _G. C. Greubel_, Sep 22 2019

%o (Sage) [(11*n+8)^10 for n in (0..20)] # _G. C. Greubel_, Sep 22 2019

%o (GAP) List([0..20], n-> (11*n+8)^10); # _G. C. Greubel_, Sep 22 2019

%Y Powers of the form (11*n+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), A017491 (m=7), A017492 (m=8), A017493 (m=9), this sequence (m=10), A017495 (m=11), A017496 (m=12).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Sep 22 2019