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%I #18 Sep 08 2022 08:44:42
%S 15625,16777216,387420489,3010936384,13841287201,46656000000,
%T 128100283921,304006671424,646990183449,1265319018496,2313060765625,
%U 4001504141376,6611856250609,10509215371264,16157819263041,24137569000000,35161828327081,50096498540544,69980368892329
%N a(n) = (11*n + 5)^6.
%H Vincenzo Librandi, <a href="/A017454/b017454.txt">Table of n, a(n) for n = 0..10000</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 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); a(0)=15625, a(1)=16777216, a(2)=387420489, a(3)=3010936384, a(4)=13841287201, a(5)=46656000000, a(6)=128100283921. - _Harvey P. Dale_, Dec 12 2013
%F From _G. C. Greubel_, Sep 18 2019: (Start)
%F G.f.: (15625 +16667841*x +270308102*x^2 +650767622*x^3 +313907097*x^4 +23810977*x^5 +46656*x^6)/(1-x)^7.
%F E.g.f.: (15625 +16761591*x +176940841*x^2 +316498490*x^3 +168957140*x^4 +31404945*x^5 +1771561*x^6)*exp(x). (End)
%p seq((11*n+5)^6, n=0..20); # _G. C. Greubel_, Sep 18 2019
%t (11*Range[0,30]+5)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {15625, 16777216, 387420489, 3010936384, 13841287201, 46656000000, 128100283921}, 30] (* _Harvey P. Dale_, Dec 12 2013 *)
%o (Magma) [(11*n+5)^6: n in [0..20]]; // _Vincenzo Librandi_, Sep 03 2011
%o (PARI) vector(20, n, (11*n-6)^6) \\ _G. C. Greubel_, Sep 18 2019
%o (Sage) [(11*n+5)^6 for n in (0..20)] # _G. C. Greubel_, Sep 18 2019
%o (GAP) List([0..20], n-> (11*n+5)^6); # _G. C. Greubel_, Sep 18 2019
%Y Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), this sequence (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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