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 A016745 a(n) = (2*n)^5. 1

%I

%S 0,32,1024,7776,32768,100000,248832,537824,1048576,1889568,3200000,

%T 5153632,7962624,11881376,17210368,24300000,33554432,45435424,

%U 60466176,79235168,102400000,130691232,164916224,205962976,254803968,312500000,380204032,459165024,550731776

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

%H Vincenzo Librandi, <a href="/A016745/b016745.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 G.f.: 32*x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1-x)^6. - _Colin Barker_, Sep 17 2012

%F E.g.f.: 32*x*(1 + 15*x + 25*x^2 + 10*x^3 + x^4)*exp(x). - _G. C. Greubel_, Sep 15 2018

%F From _Amiram Eldar_, Oct 10 2020: (Start)

%F Sum_{n>=1} 1/a(n) = zeta(5)/32.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 15*zeta(5)/512. (End)

%p A016745:=n->(2*n)^5: seq(A016745(n), n=0..50); # _Wesley Ivan Hurt_, Sep 15 2018

%t Table[(2*n)^5, {n,0,30}] (* _G. C. Greubel_, Sep 15 2018 *)

%t LinearRecurrence[{6,-15,20,-15,6,-1},{0,32,1024,7776,32768,100000},30] (* _Harvey P. Dale_, Sep 15 2019 *)

%o (MAGMA) [(2*n)^5: n in [0..30]]; // _Vincenzo Librandi_, Sep 05 2011

%o (PARI) vector(30, n, n--; (2*n)^5) \\ _G. C. Greubel_, Sep 15 2018

%Y Cf. A016757.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified May 10 20:33 EDT 2021. Contains 343780 sequences. (Running on oeis4.)