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EXAMPLE
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E.g.f.: A(x) = 1 + x + 7*x^2/2! + 159*x^3/3! + 10065*x^4/4! +...
Then e.g.f. A(x) is given by:
A(x) = 1 + L(x) + L(x)L(3x)/2! + L(x)L(3x)L(9x)/3! + L(x)L(3x)L(9x)L(27x)/4! +...
where L(x) is the e.g.f. of A177780:
. L(x) = x + 4*x^2/2! + 60*x^3/3! + 2496*x^4/4! + 276240*x^5/5! +...
. L(x) = x*d/dx log( Sum_{n>=0} 3^(n(n-1)/2)*x^n/n! )
and satisfies:
. L(x)/x = 1 + 2*L(x) + 2^2*L(x)L(3x)/2! + 2^3*L(x)L(3x)L(9x)/3! + 2^4*L(x)L(3x)L(9x)L(27x)/4! +...
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PROG
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(PARI) {a(n, q=3)=local(Lq=x+x^2, A); for(i=1, n, Lq=x*sum(m=0, n, (q-1)^m/m!*prod(k=0, m-1, subst(Lq, x, q^k*x+x*O(x^n))))); A=sum(m=0, n, 1/m!*prod(k=0, m-1, subst(Lq, x, q^k*x+x*O(x^n)))); n!*polcoeff(A, n)}
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