This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A013302 #18 Mar 05 2023 10:31:46
%S A013302 1,0,3,90,4725,396900,49116375,8428369950,1917454163625,
%T A013302 558800927685000,203054287097536875,90020733946574681250,
%U A013302 47828015945815128148125,30001210002374944020187500
%N A013302 E.g.f.: cosh(log(x+1)-arctanh(x)) (even powers only).
%C A013302 Number of degree-2n permutations without odd cycles and with even number of even cycles. E.g.f.: (2-x^2)/(2*sqrt(1-x^2)). - _Vladeta Jovovic_, Aug 10 2007
%F A013302 a(n) ~ (2*n)^(2*n)/exp(2*n). - _Vaclav Kotesovec_, Oct 19 2013
%F A013302 Conjecture: a(n) +2*(-2*n^2+2*n-3)*a(n-1) +3*(2*n-3)*(2*n-5)*a(n-2)=0. - _R. J. Mathar_, Oct 05 2014
%F A013302 Conjecture: a(n) = (4*n-5)*[(2*n-3)!!]^2 +(2*n-3)^2*a(n-1).
%e A013302 cosh(log(x+1)-arctanh(x)) = 1+3/4!*x^4+90/6!*x^6+4725/8!*x^8+...
%t A013302 nn=30;Insert[Select[Range[0,nn]!CoefficientList[Series[Cosh[Log[(1/(1-x^2))^(1/2)]],{x,0,nn}],x],#>0&],0,2] (* _Geoffrey Critzer_, Mar 10 2013 *)
%t A013302 With[{nn=30},Take[CoefficientList[Series[Cosh[Log[x+1]-ArcTanh[x]],{x,0,nn}],x] Range[ 0,nn]!,{1,-1,2}]] (* _Harvey P. Dale_, Mar 05 2023 *)
%Y A013302 Cf. A013299.
%K A013302 nonn
%O A013302 0,3
%A A013302 Patrick Demichel (patrick.demichel(AT)hp.com)