A017119 - OEIS

%I #31 Apr 25 2023 03:29:38

%S 16384,35831808,1280000000,13492928512,78364164096,319277809664,

%T 1028071702528,2799360000000,6722988818432,14645194571776,

%U 29509034655744,55784660123648,100000000000000,171382426877952,282621973446656,450766669594624,698260569735168,1054135040000000,1555363874947072,2248392813428736

%N a(n) = (8*n + 4)^7 = 4^7*(2*n + 1)^7.

%H Vincenzo Librandi, <a href="/A017119/b017119.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F a(n) = A001015(A017113(n)). - _Wesley Ivan Hurt_, Mar 10 2014

%F a(n) = 16384*A016759(n). - _Michel Marcus_, Mar 11 2014

%F 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

%F From _Amiram Eldar_, Apr 25 2023: (Start)

%F a(n) = 2^7*A016831(n).

%F Sum_{n>=0} 1/a(n) = 127*zeta(7)/2097152.

%F Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/3019898880. (End)

%p A017119:=n->(8*n+4)^7; seq(A017119(n), n=0..20); # _Wesley Ivan Hurt_, Mar 10 2014

%t Table[(8*n+4)^7, {n, 0, 20}] (* _Wesley Ivan Hurt_, Mar 10 2014 *)

%o (Magma) [(8*n+4)^7: n in [0..20] ]; // _Vincenzo Librandi_, Jul 21 2011

%o (PARI) a(n) = (8*n+4)^7; \\ _Michel Marcus_, Mar 11 2014

%Y Cf. A001015, A013665, A016759, A016831, A017113.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Michel Marcus_, Mar 11 2014