A017441 - OEIS

%I #10 Sep 08 2022 08:44:42

%S 1024,759375,11881376,69343957,254803968,714924299,1680700000,

%T 3486784401,6590815232,11592740743,19254145824,30517578125,

%U 46525874176,68641485507,98465804768,137858491849,188956800000

%N a(n) = (11*n + 4)^5.

%H G. C. Greubel, <a href="/A017441/b017441.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F From _G. C. Greubel_, Sep 18 2019: (Start)

%F G.f.: (1024 +753231*x +7340486*x^2 +9425846*x^3 +1788726*x^4 +16807*x^5 )/(1-x)^6.

%F E.g.f.: (1024 +758351*x +5181825*x^2 +5996155*x^3 +1903330*x^4 +161051*x^5)*exp(x). (End)

%p seq((11*n+4)^5, n=0..20); # _G. C. Greubel_, Sep 18 2019

%t (11 Range[0,20]+4)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1}, {1024,759375,11881376,69343957,254803968,714924299},20] (* _Harvey P. Dale_, Jan 30 2017 *)

%o (PARI) vector(20, n, (11*n-7)^5) \\ _G. C. Greubel_, Sep 18 2019

%o (Magma) [(11*n+4)^5: n in [0..20]]; // _G. C. Greubel_, Sep 18 2019

%o (Sage) [(11*n+4)^5 for n in (0..20)] # _G. C. Greubel_, Sep 18 2019

%o (GAP) List([0..20], n-> (11*n+4)^5); # _G. C. Greubel_, Sep 18 2019

%Y Powers of the form (11*n+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), this sequence (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_