%I #34 Sep 08 2022 08:44:41
%S 0,128,16384,279936,2097152,10000000,35831808,105413504,268435456,
%T 612220032,1280000000,2494357888,4586471424,8031810176,13492928512,
%U 21870000000,34359738368,52523350144,78364164096,114415582592,163840000000,230539333248,319277809664,435817657216
%N a(n) = (2*n)^7.
%H Vincenzo Librandi, <a href="/A016747/b016747.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F O.g.f.: 128*x*(1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1-x)^8. - _R. J. Mathar_, May 07 2008
%F From _Amiram Eldar_, Oct 10 2020: (Start)
%F Sum_{n>=1} 1/a(n) = zeta(7)/128.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 63*zeta(7)/8192. (End)
%p A016747:=n->(2*n)^7: seq(A016747(n), n=0..40); # _Wesley Ivan Hurt_, Sep 15 2018
%t (2*Range[0,20])^7 (* _Harvey P. Dale_, Jan 17 2011 *)
%o (Magma) [(2*n)^7: n in [0..30]]; // _Vincenzo Librandi_, Sep 05 2011
%o (PARI) vector(30, n, n--; (2*n)^7) \\ _G. C. Greubel_, Sep 15 2018
%Y Cf. A016759.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_