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%I #22 Sep 08 2022 08:44:42
%S 4096,11390625,308915776,2565726409,12230590464,42180533641,
%T 117649000000,282429536481,606355001344,1194052296529,2194972623936,
%U 3814697265625,6327518887936,10090298369529,15557597153344
%N a(n) = (11*n + 4)^6.
%H G. C. Greubel, <a href="/A017442/b017442.txt">Table of n, a(n) for n = 0..1000</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 _Harvey P. Dale_, Feb 18 2012: (Start)
%F a(0)=4096, a(1)=11390625, a(2)=308915776, a(3)=2565726409, a(4)=12230590464, a(5)=42180533641, a(6)=117649000000, 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 G.f.: ((x*(x*(x*(x*(x*(117649*x +33188681) +359208382) +642375742) +229267417) +11361953) +4096)/(1-x)^7). (End)
%F a(n) = A017437(n)^6. - _Michel Marcus_, Nov 12 2013
%F E.g.f.: (4096 +11386529*x +143069311*x^2 +278857810*x^3 +157317545*x^4 +30438639*x^5 +1771561*x^6)*exp(x). - _G. C. Greubel_, Sep 18 2019
%p A017442:=n->(11*n+4)^6; seq(A017442(n), n=0..20); # _Wesley Ivan Hurt_, Nov 11 2013
%t (11*Range[0,20]+4)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {4096, 11390625, 308915776, 2565726409, 12230590464, 42180533641, 117649000000}, 20] (* _Harvey P. Dale_, Feb 18 2012 *)
%o (PARI) vector(20, n, (11*n-7)^6) \\ _G. C. Greubel_, Sep 18 2019
%o (Magma) [(11*n+4)^6: n in [0..20]]; // _G. C. Greubel_, Sep 18 2019
%o (Sage) [(11*n+4)^6 for n in (0..20)] # _G. C. Greubel_, Sep 18 2019
%o (GAP) List([0..20], n-> (11*n+4)^6); # _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), A017441 (m=5), this sequence (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_
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