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%I #8 Dec 17 2019 02:25:07
%S 1,1,5,61,1377,49721,2625313,190735749,18246616321,2223115264945,
%T 336071395603521,61725395919953789,13537971184957280449,
%U 3494778862390292571849,1048886507411306132337889
%N E.g.f.: A(x) = exp(x*exp(2*x*exp(3*x*exp(...exp(n*x*exp(...))...)))), for n>=1.
%H Vaclav Kotesovec, <a href="/A096537/b096537.txt">Table of n, a(n) for n = 0..200</a>
%F Row sums of triangle A096542; also a(n) = A096542(n+1, 1)/(n+1) for n>=0.
%F Conjecture: a(n) ~ 2 * Pi * n^(2*n + 1/2) / (exp(n) * (exp(1) - 1)^n). - _Vaclav Kotesovec_, Dec 16 2019
%e A(x) = 1 + 1*x + 5*x^2/2! + 61*x^3/3! + 1377*x^4/4! + 49721*x^5/5! +...
%o (PARI) a(n)=local(A=exp(x));for(i=1,n,A=exp(x*(n-i+1)*A+x*O(x^n)));n!*polcoeff(A,n)
%Y Cf. A096542.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 24 2004
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