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%I #13 Feb 13 2022 06:33:18
%S 1,12,136,1650,21904,318521,5051988,86910426,1612648066,32107793135,
%T 682724688430,15439016490989,369914992674530,9359103270641290,
%U 249292192469843244,6971850327184526783,204215496402215939638,6251233458455082035922
%N Expansion of e.g.f. (exp(exp(exp(exp(x)-1)-1)-1)-1)^2 / 2.
%F a(n) = Sum_{k=1..n-1} binomial(n-1,k) * A000307(k) * A000307(n-k).
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(exp(x)-1)-1)-1)-1)^2/2))
%o (PARI) T(n, k) = if(k==0, n<=1, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
%o a(n) = sum(k=1, n-1, binomial(n-1, k)*T(k, 4)*T(n-k, 4));
%Y Column 2 of A039812.
%Y Cf. A000307, A000558, A351513, A351515.
%K nonn
%O 2,2
%A _Seiichi Manyama_, Feb 12 2022
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