A017337 a(n) = (10*n + 5)^9.
1953125, 38443359375, 3814697265625, 78815638671875, 756680642578125, 4605366583984375, 20711912837890625, 75084686279296875, 231616946283203125, 630249409724609375, 1551328215978515625, 3517876291919921875, 7450580596923828125, 14893745087865234375, 28334269484119140625
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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Magma
[(10*n+5)^9: n in [0..15]]; // Vincenzo Librandi, Aug 02 2011
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Mathematica
(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 *)
Formula
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
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^9.
a(n) = 5^9 * A016761(n).
Sum_{n>=0} 1/a(n) = 511*zeta(9)/1000000000.
Sum_{n>=0} (-1)^n/a(n) = 277*Pi^9/16128000000000. (End)