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%I #6 Feb 28 2014 03:39:25
%S 1,1,2,15,132,1545,22590,392595,7923720,182140245,4696277250,
%T 134227563855,4211901994860,143942600513985,5321725064741190,
%U 211627606517556075,9007288512919672080,408543101848039590285
%N E.g.f. A(x) satisfies: A(x) = 1 + x*exp(Integral A(x)^4 dx).
%C Compare definition of e.g.f. A(x) to the trivial statement:
%C if F(x) = 1/(1-x) then F(x) = 1 + x*exp(Integral F(x) dx).
%C Here Integral F(x) dx does not include the constant of integration.
%C Limit n->infinity (a(n)/n!)^(1/n) = 2.792845... - _Vaclav Kotesovec_, Feb 28 2014
%H Vaclav Kotesovec, <a href="/A143924/b143924.txt">Table of n, a(n) for n = 0..184</a>
%F E.g.f. derivative: A'(x) = [1 + x*A(x)^4]*(A(x) - 1)/x.
%e E.g.f. A(x) = 1+ x + 2*x^2/2! + 12*x^3/3! + 88*x^4/4! + 860*x^5/5! +...
%e A(x)^4 = 1 + 4*x + 20*x^2/2! + 144*x^3/3! +1384*x^4/4! +16400*x^5/5!+...
%e Let L(x) = Integral A(x)^4 dx where A(x) = 1 + x*exp(L(x)), then
%e L(x) = x + 4*x^2/2! + 20*x^3/3! + 144*x^4/4! + 1384*x^5/5! +...
%e exp(L(x)) = 1 + x + 5*x^2/2! + 33*x^3/3! + 297*x^4/4! + 3385*x^5/5! +...
%o (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=0,n,A=1+x*exp(intformal(A^4)));n!*polcoeff(A,n)}
%Y Cf. A143922, A143923.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 06 2008
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