OFFSET
0,3
COMMENTS
a(44) is negative. - Vaclav Kotesovec, Aug 12 2021
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..180
FORMULA
E.g.f. satisfies: A(x) = LambwertW(-y)/(-y) = Sum_{n>=0} (n+1)^(n-1)*y^n/n! where y = Series_Reversion( Integral A(x) dx ).
EXAMPLE
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 8*x^3/3! + 47*x^4/4! + 379*x^5/5! + 3824*x^6/6! +...
Related expansions.
log(A(x)) = x + x^2/2! + 4*x^3/3! + 21*x^4/4! + 168*x^5/5! + 1630*x^6/6! +...
The series reversion of the Integral A(x) dx equals log(A(x))/A(x):
log(A(x))/A(x) = x - x^2/2! + x^3/3! - 3*x^4/4! + 8*x^5/5! - 57*x^6/6! + 271*x^7/7! +...
A(Integral A(x) dx) = 1 + x + 3^1*x^2/2! + 4^2*x^3/3! + 5^3*x^4/4! + 6^4*x^5/5! +...+ (n+1)^(n-1)*x^n/n! +... = LambertW(-x)/(-x).
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(A*serreverse(intformal(A+x*O(x^n))))); n!*polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Dec 07 2013
STATUS
approved