OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..300
FORMULA
Convolution inverse of A217905.
a(n) ~ 2^(2*n - 2) * n^(n - 3/2) / (sqrt(Pi) * sqrt(1-c) * exp(n) * c^(n - 1/2) * (2-c)^(n-1)), where c = -LambertW(-2*exp(-2)) = -A226775 = 0.4063757399599599... - Vaclav Kotesovec, Aug 22 2018
EXAMPLE
O.g.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 223*x^4 + 4019*x^5 + 98071*x^6 +...
where
A(x) = 1/(1 - 1^1*0^0*x*exp(-1*0*x) - 2^2*1^1*exp(-2*1*x)*x^2/2! - 3^3*2^2*exp(-3*2*x)*x^3/3! - 4^4*3^3*exp(-4*3*x)*x^4/4! - 5^5*4^4*exp(-5*4*x)*x^5/5! +...).
simplifies to a power series in x with integer coefficients.
PROG
(PARI) {a(n)=polcoeff(1/sum(m=0, n, -m^m*(m-1)^(m-1)*x^m*exp(-m*(m-1)*x+x*O(x^n))/m!), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 14 2012
STATUS
approved