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%I #8 May 05 2024 16:17:20
%S 1,15,615,48825,6351345,1225996695,328803049575,116905182419025,
%T 53200767201206625,30152208510970120575,20822956658564943457575,
%U 17211467743309469796791625
%N Even order Taylor coefficients at x = 0 of exp( -(-2^(1/3)+(-3*x^2+2)^(1/3))/(-3*x^2+2)^(1/3) ), odd order coefficients being equal to zero.
%F In Maple notation: a(n)=subs(x=0, diff(exp(-(-2^(1/3)+(-3*x^2+2)^(1/3))/(-3*x^2+2)^(1/3)), x$2*n)), n=1, 2...
%F From _Vaclav Kotesovec_, May 05 2024: (Start)
%F a(n) ~ 2^(n - 1/2) * 3^(n + 1/8) * exp(4*n^(1/4)/3^(3/4) - 2*n - 1) * n^(2*n - 3/8).
%F a(n) = 12*(n-2)*(2*n - 1)*a(n-1) - 2*(2*n - 3)*(2*n - 1)*(27*n^2 - 135*n + 172)*a(n-2) + (2*n - 5)*(2*n - 3)*(2*n - 1)*(108*n^3 - 972*n^2 + 2928*n - 2951)*a(n-3) - 9*(n-4)*(n-3)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)*(3*n - 11)*(3*n - 10)*a(n-4). (End)
%t nmax = 20; Table[(CoefficientList[Series[E^(-1 + 1/(1 - 3*x^2/2)^(1/3)), {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[k]], {k, 3, 2*nmax, 2}] (* _Vaclav Kotesovec_, May 05 2024 *)
%Y Cf. A081020, A081021.
%K nonn,changed
%O 1,2
%A _Karol A. Penson_, Mar 01 2003
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