OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..150
FORMULA
E.g.f. A(x) satisfies: A(x) = exp(x + Integral A(x)^2 - A(x) dx).
a(n) ~ n^n * 3^(3*n/2+3/4) / (exp(n) * Pi^(n+1/2)). - Vaclav Kotesovec, Dec 19 2013
EXAMPLE
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 8*x^3/3! + 46*x^4/4! + 340*x^5/5! +...
where A(x)^2 = 1 + 2*x + 6*x^2/2! + 28*x^3/3! + 180*x^4/4! + 1460*x^5/5! +...
also, A(x)^3 = 1 + 3*x + 12*x^2/2! + 66*x^3/3! + 474*x^4/4! + 4200*x^5/5! +...
and log(A(x)) = x + x^2/2! + 4*x^3/3! + 20*x^4/4! + 134*x^5/5! + 1120*x^6/6! +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+intformal(A-A^2+A^3+x*O(x^n))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 18 2013
STATUS
approved