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%I #24 Apr 18 2023 05:02:25
%S 1953125,38443359375,3814697265625,78815638671875,756680642578125,
%T 4605366583984375,20711912837890625,75084686279296875,
%U 231616946283203125,630249409724609375,1551328215978515625,3517876291919921875,7450580596923828125,14893745087865234375,28334269484119140625
%N a(n) = (10*n + 5)^9.
%H Vincenzo Librandi, <a href="/A017337/b017337.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F G.f.: 1953125*(x+1)*(x^8 + 19672*x^7 + 1736668*x^6 + 19971304*x^5 + 49441990*x^4 + 19971304*x^3 + 1736668*x^2 + 19672*x + 1)/(x-1)^10. -_Colin Barker_, Nov 13 2012
%F From _Amiram Eldar_, Apr 18 2023: (Start)
%F a(n) = A017329(n)^9.
%F a(n) = 5^9 * A016761(n).
%F Sum_{n>=0} 1/a(n) = 511*zeta(9)/1000000000.
%F Sum_{n>=0} (-1)^n/a(n) = 277*Pi^9/16128000000000. (End)
%t (10*Range[0,20]+5)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1953125,38443359375,3814697265625,78815638671875,756680642578125,4605366583984375,20711912837890625,75084686279296875,231616946283203125,630249409724609375},20] (* _Harvey P. Dale_, Jul 23 2016 *)
%o (Magma) [(10*n+5)^9: n in [0..15]]; // _Vincenzo Librandi_, Aug 02 2011
%Y Cf. A013667, A016761, A017329.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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