A017335 a(n) = (10*n + 5)^7.
78125, 170859375, 6103515625, 64339296875, 373669453125, 1522435234375, 4902227890625, 13348388671875, 32057708828125, 69833729609375, 140710042265625, 266001988046875, 476837158203125, 817215093984375, 1347646586640625, 2149422977421875, 3329565857578125
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
Programs
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Magma
[(10*n+5)^7: n in [0..25]]; // Vincenzo Librandi, Aug 02 2011
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Mathematica
Table[(10*n + 5)^7, {n, 0, 20}] (* Amiram Eldar, Apr 18 2023 *)
Formula
G.f.: 78125*(x+1)*(x^6 + 2178*x^5 + 58479*x^4 + 201244*x^3 + 58479*x^2 + 2178*x + 1)/(x-1)^8. - Colin Barker, Nov 13 2012
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^7.
a(n) = 5^7 * A016759(n).
Sum_{n>=0} 1/a(n) = 127*zeta(7)/10000000.
Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/14400000000. (End)