A017332 - OEIS

%I #24 Aug 20 2024 13:20:59

%S 625,50625,390625,1500625,4100625,9150625,17850625,31640625,52200625,

%T 81450625,121550625,174900625,244140625,332150625,442050625,577200625,

%U 741200625,937890625,1171350625,1445900625,1766100625,2136750625,2562890625,3049800625,3603000625

%N a(n) = (10*n + 5)^4.

%H Vincenzo Librandi, <a href="/A017332/b017332.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: -625*(x^4 + 76*x^3 + 230*x^2 + 76*x+1)/(x-1)^5. - _Colin Barker_, Nov 14 2012

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

%F a(n) = A017329(n)^4.

%F a(n) = 5^4 * A016756(n).

%F Sum_{n>=0} 1/a(n) = Pi^4/60000. (End)

%t Table[(10*n + 5)^4, {n, 0, 30}] (* _Amiram Eldar_, Apr 18 2023 *)

%t LinearRecurrence[{5,-10,10,-5,1},{625,50625,390625,1500625,4100625},30] (* _Harvey P. Dale_, Aug 20 2024 *)

%o (Magma) [(10*n+5)^4: n in [0..35]]; // _Vincenzo Librandi_, Aug 02 2011

%Y Cf. A016756, A017329.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_