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%I #23 Sep 08 2022 08:44:42
%S 531441,64000000,887503681,5489031744,22164361129,68719476736,
%T 177978515625,404567235136,832972004929,1586874322944,2839760855281,
%U 4826809000000,7858047974841,12332795428864,18755369578009
%N a(n) = (11*n + 9)^6.
%H G. C. Greubel, <a href="/A017502/b017502.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 _G. C. Greubel_, Oct 28 2019: (Start)
%F G.f.: (531441 + 60279913*x + 450663942*x^2 + 601905542*x^3 + 157316657*x^4 + 4826361*x^5 + 64*x^6)/(1-x)^7.
%F E.g.f.: (531441 + 63468559*x + 380017561*x^2 + 502998210*x^3 + 219907820*x^4 + 35270169*x^5 + 1771561*x^6)*exp(x). (End)
%p seq((11*n+9)^6, n=0..20); # _G. C. Greubel_, Oct 28 2019
%t (11Range[0,20]+9)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {531441,64000000,887503681,5489031744,22164361129,68719476736, 177978515625}, 20] (* _Harvey P. Dale_, Dec 06 2018 *)
%o (Maxima) makelist((11*n+9)^6, n, 0, 30); /* _Martin Ettl_, Oct 21 2012 */
%o (PARI) vector(21, n, (11*n-2)^6) \\ _G. C. Greubel_, Oct 28 2019
%o (Magma) [(11*n+9)^6: n in [0..20]]; // _G. C. Greubel_, Oct 28 2019
%o (Sage) [(11*n+9)^6 for n in (0..20)] # _G. C. Greubel_, Oct 28 2019
%o (GAP) List([0..20], n-> (11*n+9)^6); # _G. C. Greubel_, Oct 28 2019
%Y Powers of the form (11*n+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), this sequence (m=6), A017503 (m=7), A017504 (m=8), A017505 (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).
%Y Subsequence of A001014.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_