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%I #23 Apr 21 2023 05:46:53
%S 256,1679616,100000000,1475789056,11019960576,54875873536,
%T 208827064576,656100000000,1785793904896,4347792138496,9682651996416,
%U 20047612231936,39062500000000,72301961339136,128063081718016,218340105584896,360040606269696,576480100000000,899194740203776
%N a(n) = (4*n + 2)^8.
%H Vincenzo Librandi, <a href="/A016832/b016832.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F From _Harvey P. Dale_, May 20 2011: (Start)
%F a(0)=256, a(1)=1679616, a(2)=100000000, a(3)=1475789056, a(4)=11019960576, a(5)=54875873536, a(6)=208827064576, a(7)=656100000000, a(8)=1785793904896, a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).
%F G.f.: -((256*(1 + 6552*x + 331612*x^2 + 2485288*x^3 + 4675014*x^4 + 2485288*x^5 + 331612*x^6 + 6552*x^7 + x^8))/(-1+x)^9). (End)
%F From _Amiram Eldar_, Apr 21 2023: (Start)
%F a(n) = A016825(n)^8.
%F a(n) = 2^8*A016760(n).
%F Sum_{n>=0} 1/a(n) = 17*Pi^8/41287680. (End)
%t (4Range[0,20]+2)^8 (* _Harvey P. Dale_, May 20 2011 *)
%o (Magma) [(4*n+2)^8: n in [0..30] ]; // _Vincenzo Librandi_, May 23 2011
%Y Cf. A016760, A016825.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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