A233338 - OEIS

A233338

E.g.f. satisfies: A(x) = exp( A(x) * Integral A(-x) dx ).

1, 1, 2, 9, 53, 464, 4687, 61479, 886258, 15524575, 291505295, 6394185264, 148118036273, 3904856867873, 107649269291290, 3315317751482457, 106031435475881053, 3736096118740095232, 136008862573108676543, 5396412601537476189351, 220341893750220550211546, 9721518437451024623900879

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

EXAMPLE

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 53*x^4/4! + 464*x^5/5! + 4687*x^6/6! +...

Related expansions.

log(A(x)) = x + x^2/2! + 5*x^3/3! + 23*x^4/4! + 223*x^5/5! + 1933*x^6/6! +...

log(A(x))/A(x) = x - x^2/2! + 2*x^3/3! - 9*x^4/4! + 53*x^5/5! - 464*x^6/6! +...

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(A*intformal(subst(A, x, -x)+x*O(x^n)))); n!*polcoeff(A, n)}