OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..40
FORMULA
Logarithmic derivative yields A224733.
a(n) ~ exp(-1/8) * 2^(2*n^2) / (Pi^(n/2) * n^(1 + n/2)). - Vaclav Kotesovec, Jan 26 2015
a(n) ~ (binomial(2*n,n))^n / n. - Vaclav Kotesovec, Jan 26 2015
EXAMPLE
G.f.: A(x) = 1 + 2*x + 20*x^2 + 2704*x^3 + 6008032*x^4 + 203263062688*x^5 +...
where
log(A(x)) = 2*x + 6^2*x^2/2 + 20^3*x^3/3 + 70^4*x^4/4 + 252^5*x^5/5 + 924^6*x^6/6 + 3432^7*x^7/7 + 12870^8*x^8/8 +...+ A000984(n)^n*x^n/n +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(k=1, n, binomial(2*k, k)^k*x^k/k)+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 16 2013
STATUS
approved