A016746 - OEIS

%I #26 Sep 08 2022 08:44:41

%S 0,64,4096,46656,262144,1000000,2985984,7529536,16777216,34012224,

%T 64000000,113379904,191102976,308915776,481890304,729000000,

%U 1073741824,1544804416,2176782336,3010936384,4096000000,5489031744,7256313856,9474296896,12230590464,15625000000

%N a(n) = (2*n)^6.

%H Vincenzo Librandi, <a href="/A016746/b016746.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F G.f.: 64*x*(1+x)*(x^4 + 56*x^3 + 246*x^2 + 56*x + 1) / (1-x)^7. - _R. J. Mathar_, May 01 2015

%F E.g.f.: 64*x*(1 + 31*x + 90*x^2 + 65*x^3 + 15*x^4 + x^5)*exp(x). - _G. C. Greubel_, Sep 15 2018

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

%F Sum_{n>=1} 1/a(n) = Pi^6/60480.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 31*Pi^6/1935360. (End)

%p A016746:=n->(2*n)^6: seq(A016746(n), n=0..50); # _Wesley Ivan Hurt_, Sep 15 2018

%t Table[(2*n)^6, {n,0,30}] (* _G. C. Greubel_, Sep 15 2018 *)

%o (Magma) [(2*n)^6: n in [0..30]]; // _Vincenzo Librandi_, Sep 05 2011

%o (PARI) vector(30, n, n--; (2*n)^6) \\ _G. C. Greubel_, Sep 15 2018

%Y Cf. A016758.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_