A017119 a(n) = (8*n + 4)^7 = 4^7*(2*n + 1)^7.
16384, 35831808, 1280000000, 13492928512, 78364164096, 319277809664, 1028071702528, 2799360000000, 6722988818432, 14645194571776, 29509034655744, 55784660123648, 100000000000000, 171382426877952, 282621973446656, 450766669594624, 698260569735168, 1054135040000000, 1555363874947072, 2248392813428736
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
[(8*n+4)^7: n in [0..20] ]; // Vincenzo Librandi, Jul 21 2011
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Maple
A017119:=n->(8*n+4)^7; seq(A017119(n), n=0..20); # Wesley Ivan Hurt, Mar 10 2014
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Mathematica
Table[(8*n+4)^7, {n, 0, 20}] (* Wesley Ivan Hurt, Mar 10 2014 *) -
PARI
a(n) = (8*n+4)^7; \\ Michel Marcus, Mar 11 2014
Formula
a(n) = 16384*A016759(n). - Michel Marcus, Mar 11 2014
G.f.: 16384*(x+1)*(x^6 + 2178*x^5 + 58479*x^4 + 201244*x^3 + 58479*x^2 + 2178*x + 1) / (x-1)^8. - Colin Barker, Mar 11 2014
From Amiram Eldar, Apr 25 2023: (Start)
a(n) = 2^7*A016831(n).
Sum_{n>=0} 1/a(n) = 127*zeta(7)/2097152.
Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/3019898880. (End)
Extensions
More terms from Michel Marcus, Mar 11 2014