%I #14 Jan 26 2015 13:21:37

%S 1,2,20,2704,6008032,203263062688,103724721990326528,

%T 801185400238209125917312,94088900962948953837864576996352,

%U 168691065596220817138271126002845218561536,4634314586972355372645450331391809316221983940020224

%N G.f.: exp( Sum_{n>=1} binomial(2*n,n)^n * x^n/n ).

%H Vaclav Kotesovec, <a href="/A224732/b224732.txt">Table of n, a(n) for n = 0..40</a>

%F Logarithmic derivative yields A224733.

%F a(n) ~ exp(-1/8) * 2^(2*n^2) / (Pi^(n/2) * n^(1 + n/2)). - _Vaclav Kotesovec_, Jan 26 2015

%F a(n) ~ (binomial(2*n,n))^n / n. - _Vaclav Kotesovec_, Jan 26 2015

%e G.f.: A(x) = 1 + 2*x + 20*x^2 + 2704*x^3 + 6008032*x^4 + 203263062688*x^5 +...

%e where

%e 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 +...

%o (PARI) {a(n)=polcoeff(exp(sum(k=1,n,binomial(2*k,k)^k*x^k/k)+x*O(x^n)),n)}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A200002, A224733, A201556, A224734, A224735, A224736, A000984.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 16 2013