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Even order Taylor coefficients at x = 0 of exp( (sqrt(2)-sqrt(-2*x^2+2))/(-2*x^2+2)^(1/2) ), odd order coefficients being equal to zero.
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%I #14 May 05 2024 11:44:57

%S 1,12,375,22155,2113020,295956045,57148456365,14541025999500,

%T 4712328126180675,1894168782984052575,924528651354021413700,

%U 538492713580088225984025

%N Even order Taylor coefficients at x = 0 of exp( (sqrt(2)-sqrt(-2*x^2+2))/(-2*x^2+2)^(1/2) ), odd order coefficients being equal to zero.

%H G. C. Greubel, <a href="/A081021/b081021.txt">Table of n, a(n) for n = 1..224</a>

%F In Maple notation: a(n)=subs(x=0, diff(exp((sqrt(2)-sqrt(-2*x^2+2))/(-2*x^2+2)^(1/2), x$2*n)), n=1, 2...

%F From _Vaclav Kotesovec_, May 05 2024: (Start)

%F a(n) ~ 2^(2*n + 2/3) * exp(3*n^(1/3)/2^(2/3) - 2*n - 1) * n^(2*n - 1/3) / sqrt(3).

%F a(n) = 3*(2*n - 3)*(2*n - 1)*a(n-1) - (2*n - 3)*(2*n - 1)*(12*n^2 - 48*n + 47)*a(n-2) + 4*(n-3)*(n-2)*(2*n - 5)^2*(2*n - 3)*(2*n - 1)*a(n-3). (End)

%t Rest[With[{nmax = 100}, CoefficientList[Series[Exp[(Sqrt[2] - Sqrt[2 - 2*x^2])/(Sqrt[2 - 2*x^2]) ], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; -1 ;; 2]]] (* _G. C. Greubel_, Sep 11 2018 *)

%Y Cf. A081020.

%K nonn

%O 1,2

%A _Karol A. Penson_, Mar 01 2003