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A088026 Number of "sets of even lists" for even n, cf. A000262.

%I A088026 #31 Feb 19 2022 14:37:35
%S A088026 1,2,36,1560,122640,15150240,2695049280,650948538240,204637027795200,
%T A088026 81098021561356800,39516616693678924800,23204736106751520921600,
%U A088026 16152539421202464036556800,13145716394493318293898240000,12363004898960780220305909760000
%N A088026 Number of "sets of even lists" for even n, cf. A000262.
%H A088026 Vincenzo Librandi, <a href="/A088026/b088026.txt">Table of n, a(n) for n = 0..100</a>
%F A088026 E.g.f.: exp(x^2/(1-x^2)) (even powers only, see PARI code).
%F A088026 E.g.f.: exp(x^2/(1-x^2)) = 4/(2-(x^2/(1-x^2))*G(0))-1 where G(k) = 1 - x^4/(x^4 + 4*(1-x^2)^2*(2*k+1)*(2*k+3)/G(k+1) ) (continued fraction). - _Sergei N. Gladkovskii_, Dec 10 2012
%F A088026 a(n) ~ 2^(2*n) * n^(2*n-1/4) * exp(sqrt(4*n)-2*n-1/2). - _Vaclav Kotesovec_, Feb 25 2014
%F A088026 D-finite with recurrence a(n) -2*(2*n-1)^2*a(n-1) +4*(n-1)*(n-2)*(2*n-1)*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Feb 01 2022
%F A088026 a(n) = A206703(2n,n). - _Alois P. Heinz_, Feb 19 2022
%p A088026 b:= proc(n) option remember; `if`(n=0, 1, add((i->
%p A088026       b(n-i)*binomial(n-1, i-1)*i!)(2*j), j=1..n/2))
%p A088026     end:
%p A088026 a:= n-> b(2*n):
%p A088026 seq(a(n), n=0..14);  # _Alois P. Heinz_, Feb 01 2022
%t A088026 Table[n!*SeriesCoefficient[E^(x^2/(1-x^2)),{x,0,n}],{n,0,40,2}] (* _Vaclav Kotesovec_, Feb 25 2014 *)
%o A088026 (PARI)
%o A088026 x='x+O('x^66); /* (half) that many terms */
%o A088026 v=Vec(serlaplace(exp(x^2/(1-x^2))));
%o A088026 vector(#v\2,n, v[2*n-1])
%o A088026 /* _Joerg Arndt_, Jul 29 2012 */
%Y A088026 Cf. A052845, A088009, A206703.
%K A088026 nonn
%O A088026 0,2
%A A088026 _Vladeta Jovovic_, Nov 02 2003
%E A088026 More terms from _Joerg Arndt_, Jul 29 2012.