%I #20 Jun 26 2025 10:45:16

%S 243,100000,1419857,7962624,28629151,79235168,184528125,380204032,

%T 714924299,1252332576,2073071593,3276800000,4984209207,7339040224,

%U 10510100501,14693280768,20113571875,27027081632,35723051649,46525874176

%N a(n) = (7*n + 3)^5.

%H Vincenzo Librandi, <a href="/A017021/b017021.txt">Table of n, a(n) for n = 0..10000</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_, Oct 17 2023: (Start)

%F G.f.: (243 + 98542*x + 823502*x^2 + 938622*x^3 + 154907*x^4 + 1024*x^5)/(1-x)^6.

%F E.g.f.: (243 + 99757*x + 610050*x^2 + 667135*x^3 + 204085*x^4 + 16807*x^5)*exp(x). (End)

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - _Wesley Ivan Hurt_, Jun 26 2025

%t (7*Range[0,20]+3)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{243,100000,1419857,7962624,28629151,79235168},20] (* _Harvey P. Dale_, Aug 27 2017 *)

%o (Magma) [(7*n+3)^5: n in [0..35]]; // _Vincenzo Librandi_, Jul 14 2011

%o (SageMath) [(7*n+3)^5 for n in range(41)] # _G. C. Greubel_, Oct 17 2023

%Y Cf. A017017 - A017020, A017022 - A017028.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_