OFFSET
0,3
COMMENTS
Compare the e.g.f. to:
(1) W(x) = exp(x/W(-x*W(x)^2)^1) when W(x) = Sum_{n>=0} (1*n+1)^(n-1)*x^n/n!.
(2) W(x) = exp(x/W(-x*W(x)^4)^2) when W(x) = Sum_{n>=0} (2*n+1)^(n-1)*x^n/n!.
(3) W(x) = exp(x/W(-x*W(x)^6)^3) when W(x) = Sum_{n>=0} (3*n+1)^(n-1)*x^n/n!.
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 41*x^4/4! + 76*x^5/5! - 2183*x^6/6! +...
Related expansions:
1/A(-x*A(x)) = 1 + x + x^2/2! + x^3/3! - 23*x^4/4! - 419*x^5/5! - 5159*x^6/6! +...
The logarithm of the e.g.f., log(A(x) = x/A(-x*A(x)), begins:
log(A(x)) = x + 2*x^2/2! + 3*x^3/3! + 4*x^4/4! - 115*x^5/5! - 2514*x^6/6! - 36113*x^7/7! +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(x/subst(A, x, -x*A+x*O(x^n)))); n!*polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jun 05 2012
STATUS
approved