%I #6 Sep 14 2021 09:45:09
%S 1,1,12,429,37876,6761065,2136044046,1089769282777,840138009989496,
%T 930785292596431665,1424838078730777692250,2919980132606043561607201,
%U 7805899106468938819037737572,26636112093062499073393688363737,113900544542333346101951507567405622
%N Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - 4*x*exp(x)/(1 - 9*x*exp(x)/(1 - 16*x*exp(x)/(1 - ...))))), a continued fraction.
%F a(n) ~ 2^(4*n + 7/2) * n^(3*n + 1) / (exp(3*n) * Pi^(2*n)).
%t nmax = 20; CoefficientList[Series[1/(1 + ContinuedFractionK[-k^2*x*Exp[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] * Range[0, nmax]!
%Y Cf. A295240.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Sep 14 2021
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