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%I #12 Dec 19 2013 14:13:58
%S 1,1,2,8,46,340,3080,33020,408760,5737600,90041480,1562155760,
%T 29688699040,613378208080,13687826477600,328103392918400,
%U 8407745335871200,229363476365320000,6636554484183747200,203007064284501963200,6545704564601880726400,221887453210925123353600
%N E.g.f. A(x) satisfies: A'(x) = A(x) - A(x)^2 + A(x)^3.
%H Vaclav Kotesovec, <a href="/A229559/b229559.txt">Table of n, a(n) for n = 0..150</a>
%F E.g.f. A(x) satisfies: A(x) = exp(x + Integral A(x)^2 - A(x) dx).
%F a(n) ~ n^n * 3^(3*n/2+3/4) / (exp(n) * Pi^(n+1/2)). - _Vaclav Kotesovec_, Dec 19 2013
%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 8*x^3/3! + 46*x^4/4! + 340*x^5/5! +...
%e where A(x)^2 = 1 + 2*x + 6*x^2/2! + 28*x^3/3! + 180*x^4/4! + 1460*x^5/5! +...
%e also, A(x)^3 = 1 + 3*x + 12*x^2/2! + 66*x^3/3! + 474*x^4/4! + 4200*x^5/5! +...
%e and log(A(x)) = x + x^2/2! + 4*x^3/3! + 20*x^4/4! + 134*x^5/5! + 1120*x^6/6! +...
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+intformal(A-A^2+A^3+x*O(x^n))); n!*polcoeff(A, n)}
%o for(n=0, 30, print1(a(n), ", "))
%Y Cf. A124212.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 18 2013
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