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EXAMPLE
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E.g.f.: A(x) = x + 10*x^2/2! + 315*x^3/3! + 16520*x^4/4! + 1212775*x^5/5! +...
where A(6*x - 5*x*exp(x)) = x.
Also we have the related infinite series.
O.g.f.: F(x) = x + 10*x^2 + 315*x^3 + 16520*x^4 + 1212775*x^5 +...
where F(x)/x = 1/6 + 5/(6-x)^2 + 5^2/(6-2*x)^3 + 5^3/(6-3*x)^4 + 5^4/(6-4*x)^5 +...
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PROG
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(PARI) {a(n) = local(A=x); A = serreverse(6*x - 5*x*exp(x +x*O(x^n) )); n!*polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", "))
(PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D}
{a(n)=local(A=x); A = x + sum(m=1, n, Dx(m-1, 5^m*(exp(x+x*O(x^n))-1)^m * x^m/m!)); n!*polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
(PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D}
{a(n)=local(A=x+x^2+x*O(x^n)); A = x*exp(sum(m=1, n, Dx(m-1, 5^m*(exp(x+x*O(x^n))-1)^m * x^(m-1)/m!)+x*O(x^n))); n!*polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
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