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A017117 a(n) = (8*n + 4)^5.

%I A017117 #20 Apr 25 2023 05:27:36
%S A017117 1024,248832,3200000,17210368,60466176,164916224,380204032,777600000,
%T A017117 1453933568,2535525376,4182119424,6590815232,10000000000,14693280768,
%U A017117 21003416576,29316250624,40074642432,53782400000,71008211968,92389579776,118636749824,150536645632,188956800000
%N A017117 a(n) = (8*n + 4)^5.
%H A017117 Vincenzo Librandi, <a href="/A017117/b017117.txt">Table of n, a(n) for n = 0..10000</a>
%H A017117 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A017117 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)=1024, a(1)=248832, a(2)=3200000, a(3)=17210368, a(4)=60466176, a(5)=164916224. - _Harvey P. Dale_, Nov 24 2012
%F A017117 G.f.: 1024*(1+x)*(x^4 + 236*x^3 + 1446*x^2 + 236*x + 1) / (x-1)^6. - _R. J. Mathar_, May 08 2015
%F A017117 From _Amiram Eldar_, Apr 25 2023: (Start)
%F A017117 a(n) = A017113(n)^5.
%F A017117 a(n) = 2^5*A016829(n) = 2^10*A016757(n).
%F A017117 Sum_{n>=0} 1/a(n) = 31*zeta(5)/32768.
%F A017117 Sum_{n>=0} (-1)^n/a(n) = 5*Pi^5/1572864. (End)
%t A017117 (8*Range[0,20]+4)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1024,248832,3200000,17210368,60466176,164916224},20] (* _Harvey P. Dale_, Nov 24 2012 *)
%o A017117 (Magma) [(8*n+4)^5: n in [0..30] ]; // _Vincenzo Librandi_, Jul 21 2011
%Y A017117 Cf. A013663, A016757, A016829, A017113.
%K A017117 nonn,easy
%O A017117 0,1
%A A017117 _N. J. A. Sloane_