A017339 - OEIS

%I #22 Apr 18 2023 05:02:18

%S 48828125,8649755859375,2384185791015625,96549157373046875,

%T 1532278301220703125,13931233916552734375,87507831740087890625,

%U 422351360321044921875,1673432436896142578125,5688000922764599609375,17103393581163134765625,46523913960640966796875,116415321826934814453125

%N a(n) = (10*n + 5)^11.

%H Vincenzo Librandi, <a href="/A017339/b017339.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

%F G.f.: 48828125*(x+1)*(x^10 + 177134*x^9 + 46525293*x^8 + 1356555432*x^7 + 9480267666*x^6 + 19107752148*x^5 + 9480267666*x^4 + 1356555432*x^3 + 46525293*x^2 + 177134*x + 1)/(x-1)^12. - _Colin Barker_, Nov 14 2012

%F From _Amiram Eldar_, Apr 18 2023: (Start)

%F a(n) = A017329(n)^11.

%F a(n) = 5^11 * A016763(n).

%F Sum_{n>=0} 1/a(n) = 2047*zeta(11)/100000000000.

%F Sum_{n>=0} (-1)^n/a(n) = 50521*Pi^11/725760000000000000. (End)

%t Table[(10*n + 5)^11, {n, 0, 15}] (* _Amiram Eldar_, Apr 18 2023 *)

%o (Magma) [(10*n+5)^11: n in [0..10]]; // _Vincenzo Librandi_, Aug 02 2011

%Y Cf. A013669, A016763, A017329.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_