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A096537 E.g.f.: A(x) = exp(x*exp(2*x*exp(3*x*exp(...exp(n*x*exp(...))...)))), for n>=1.

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