OFFSET
0,3
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 18*x^3/3! + 170*x^4/4! + 2240*x^5/5! +...
where
A(x) = 1 + [Integral A(x) dx] + [Integral A(x) dx]*[Integral A(x)^2 dx] + [Integral A(x) dx]*[Integral A(x)^2 dx]*[Integral A(x)^3 dx] +...
Related series:
A(x)^2 = 1 + 2*x + 8*x^2/2! + 54*x^3/3! + 538*x^4/4! + 7260*x^5/5! +...
A(x)^3 = 1 + 3*x + 15*x^2/2! + 114*x^3/3! + 1212*x^4/4! + 16950*x^5/5! +...
A(x)^4 = 1 + 4*x + 24*x^2/2! + 204*x^3/3! + 2324*x^4/4! + 33920*x^5/5! +...
A(x)^5 = 1 + 5*x + 35*x^2/2! + 330*x^3/3! + 4030*x^4/4! + 61620*x^5/5! +...
A(x)^6 = 1 + 6*x + 48*x^2/2! + 498*x^3/3! + 6510*x^4/4! + 104460*x^5/5! +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, prod(k=1, m, intformal(A^k+x*O(x^n))))); n!*polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 22 2013
STATUS
approved