OFFSET
0,3
EXAMPLE
O.g.f.: A(x) = 1 + x + 6*x^2 + 53*x^3 + 931*x^4 + 21847*x^5 + 791525*x^6 +...
where
A(x) = exp(-4*x) + 5*x*A(x)*exp(-5*x*A(x)) + 6^2*x^2*A(2*x)^2/2!*exp(-6*x*A(2*x)) + 7^3*x^3*A(3*x)^3/3!*exp(-7*x*A(3*x)) + 8^4*x^4*A(4*x)^4/4!*exp(-8*x*A(4*x)) + 9^5*x^5*A(5*x)^5/5!*exp(-9*x*A(5*x)) +...
simplifies to a power series in x with integer coefficients.
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(k=0, n, (k+4)^k*x^k*subst(A, x, k*x)^k/k!*exp(-(k+4)*x*subst(A, x, k*x)+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 15 2013
STATUS
approved