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a(n) = (10*n + 2)^5.
1

%I #15 Sep 08 2022 08:44:42

%S 32,248832,5153632,33554432,130691232,380204032,916132832,1934917632,

%T 3707398432,6590815232,11040808032,17623416832,27027081632,

%U 40074642432,57735339232,81136812032,111577100832

%N a(n) = (10*n + 2)^5.

%H Vincenzo Librandi, <a href="/A017297/b017297.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 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); a(0)=32, a(1)=248832, a(2)=5153632, a(3)=33554432, a(4)=130691232, a(5)=380204032. - _Harvey P. Dale_, May 24 2015

%F G.f.: (32*(1 + 7770*x + 114410*x^2 + 198890*x^3 + 52905*x^4 + 1024*x^5))/(-1+x)^6. - _Harvey P. Dale_, May 24 2015

%t (10*Range[0,20]+2)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{32,248832,5153632,33554432,130691232,380204032},20] (* _Harvey P. Dale_, May 24 2015 *)

%o (Magma) [(10*n+2)^5: n in [0..25]]; // _Vincenzo Librandi_, Jul 30 2011

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_