%I #18 Sep 08 2022 08:44:42
%S 9765625,1099511627776,205891132094649,6278211847988224,
%T 79792266297612001,604661760000000000,3255243551009881201,
%U 13744803133596058624,48398230717929318249,148024428491834392576
%N a(n) = (11*n + 5)^10.
%H Vincenzo Librandi, <a href="/A017458/b017458.txt">Table of n, a(n) for n = 0..10000</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 19 2019: (Start)
%F G.f.: (9765625 +1099404205901*x +193797041298488*x^2 +4073880923146640* x^3 +21874532039020442*x^4 +38639279895450554*x^5 +24069986191404704*x^6 +4993111339147592*x^7 +274024159430165*x^8 +2015328772513*x^9 +60466176* x^10)/(1-x)^11.
%F E.g.f.: (9765625 +1099501862151*x +101846059302361*x^2 +943972829470330* x^3 +2329598652561730*x^4 +2220242776827075*x^5 +974547942271827*x^6 + 214025260632480*x^7 +23938528035675*x^8 +1285081491595*x^9 +25937424601* x^10)*exp(x). (End)
%p seq((11*n+5)^10, n=0..20); # _G. C. Greubel_, Sep 19 2019
%t (11*Range[21] -6)^10 (* _G. C. Greubel_, Sep 19 2019 *)
%t LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{9765625,1099511627776,205891132094649,6278211847988224,79792266297612001,604661760000000000,3255243551009881201,13744803133596058624,48398230717929318249,148024428491834392576,404555773570791015625},20] (* _Harvey P. Dale_, Aug 19 2020 *)
%o (Magma) [(11*n+5)^10: n in [0..10]]; // _Vincenzo Librandi_, Sep 03 2011
%o (PARI) vector(20, n, (11*n-6)^10) \\ _G. C. Greubel_, Sep 19 2019
%o (Sage) [(11*n+5)^10 for n in (0..20)] # _G. C. Greubel_, Sep 19 2019
%o (GAP) List([0..20], n-> (11*n+5)^10); # _G. C. Greubel_, Sep 19 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), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), this sequence (m=10), A017459 (m=11), A017460 (m=12).
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
|