OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..300
Mathematics StackExchange, Taylor series about x=e of x^y=y^x
FORMULA
y = - (x/log(e*x)) * W(-log(e*x)/(e*x)) where W is the main branch of the Lambert W function for x > 1 and the "-1" branch for x < 1.
EXAMPLE
y = 1 - (x-1) + (5/3)*(x-1)^2 - (25/9)*(x-1)^3 + (1243/270)*(x-1)^4 - (1229/162)*(x-1)^5 + ....
MAPLE
y:= -x*LambertW(-(1 + ln(x))*exp(-1)/x)/(1 + ln(x)):
S:= series(y, x=1, 31) assuming x>1:
seq(denom(coeff(S, x-1, j)), j=0..30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Oct 04 2019
STATUS
approved