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%I #20 Sep 28 2021 19:54:37
%S 1,1,9,195,7665,473445,42110145,5085535455,799363389825,
%T 158394573362025,38590445989920825,11330437552124766075,
%U 3943491069629507821425,1604701708312172643298125,754577935727586683368280625,405920422302165926006881404375
%N Even order Taylor coefficients at x = 0 of exp(-x^2/(x^2-2)), odd order coefficients being equal to zero.
%F E.g.f.: exp(-x^2/(x^2-2)) (even orders only).
%F a(n) ~ 2^n * n^(2*n - 1/4) / exp(2*n - 2*sqrt(n) + 1/2). - _Vaclav Kotesovec_, Sep 27 2021
%p a:= n-> (2*n)!*coeff(series(exp(-x^2/(x^2-2)), x, 2*n+1), x, 2*n):
%p seq(a(n), n=0..16); # _Alois P. Heinz_, Sep 27 2021
%t terms = 12;
%t m = 2*terms+2;
%t Partition[CoefficientList[Exp[-x^2/(x^2-2)] + O[x]^(m+2), x]*Range[0,m]!, 2][[2 ;; , 1]] (* _Jean-François Alcover_, Sep 27 2021 *)
%o (PARI) my(x='x+O('x^35)); select(x->(x!=0), Vec(serlaplace(exp(-x^2/(x^2-2))))) \\ _Michel Marcus_, Sep 27 2021
%K nonn
%O 0,3
%A _Karol A. Penson_, Mar 01 2003
%E a(0)=1 prepended by _Alois P. Heinz_, Sep 27 2021
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