cp's OEIS Frontend

A171638 Denominator of 1/(n-2)^2 - 1/(n+2)^2.

%I A171638 #27 Aug 14 2022 03:02:34
%S A171638 0,25,9,441,64,2025,225,5929,576,13689,1225,27225,2304,48841,3969,
%T A171638 81225,6400,127449,9801,190969,14400,275625,20449,385641,28224,525625,
%U A171638 38025,700569,50176,915849,65025,1177225,82944,1490841
%N A171638 Denominator of 1/(n-2)^2 - 1/(n+2)^2.
%C A171638 Fifth column of an array of denominators related to the energies of the hydrogen spectrum, mentioned in A171522. At n=2, the defining formula has a pole and is replaced by 0 to conform with A171621 and A099761.
%H A171638 G. C. Greubel, <a href="/A171638/b171638.txt">Table of n, a(n) for n = 2..5000</a>
%H A171638 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-10,0,10,0,-5,0,1).
%F A171638 a(n) = (A171621(n))^2.
%F A171638 a(2*n+2) = A099761(n).
%F A171638 G.f.: -((x(25+9*x+316*x^2+19*x^3+70*x^4-5*x^5-36*x^6+x^7+9*x^8))/((-1+x)^5 (1+x)^5)). - _Harvey P. Dale_, Sep 07 2021
%F A171638 Sum_{n>=3} 1/a(n) = 19*Pi^2/192 - 115/144. - _Amiram Eldar_, Aug 14 2022
%p A171638 A061037 := proc(n) 1/4-1/n^2 ; numer(%) ; end proc:
%p A171638 A171621 := proc(n) if n mod 4 = 2 then 4*A061037(n) ; else A061037(n) ; end if; end proc:
%p A171638 A171638 := proc(n) A171621(n)^2 ; end proc:
%p A171638 seq(A171638(n),n=2..90) ; # _R. J. Mathar_, Apr 02 2011
%t A171638 Table[If[n == 2, 0, Denominator[1/(n-2)^2 - 1/(n+2)^2]], {n, 2, 50}] (* _G. C. Greubel_, Sep 20 2018 *)
%t A171638 LinearRecurrence[{0,5,0,-10,0,10,0,-5,0,1},{0,25,9,441,64,2025,225,5929,576,13689},50] (* _Harvey P. Dale_, Sep 07 2021 *)
%o A171638 (Magma) [0] cat [Denominator((1/(n-2)^2 -1/(n+2)^2)): n in [3..350]]; // _Bruno Berselli_, Apr 05 2011
%o A171638 (PARI) for(n=2,100, print1(if(n==2,0, denominator(1/(n-2)^2 - 1/(n+2)^2)), ", ")) \\ _G. C. Greubel_, Sep 20 2018
%Y A171638 Cf. A099761, A171621.
%K A171638 nonn,frac,easy
%O A171638 2,2
%A A171638 _Paul Curtz_, Dec 13 2009