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%I #3 Apr 16 2013 21:52:10
%S 1,16,776,64384,7151460,947788608,141137282720,22814994697728,
%T 3918995299504938,705339416079749024,131725296229995045840,
%U 25348575698532710671104,5000341179482293108254824,1007144334380887781805059200,206487157000689985136888031296
%N G.f.: exp( Sum_{n>=1} binomial(2*n,n)^4 * x^n/n ).
%F Logarithmic derivative yields A186420.
%e G.f.: A(x) = 1 + 16*x + 776*x^2 + 64384*x^3 + 7151460*x^4 + 947788608*x^5 +...
%e where
%e log(A(x)) = 2^4*x + 6^4*x^2/2 + 20^4*x^3/3 + 70^4*x^4/4 + 252^4*x^5/5 + 924^4*x^6/6 + 3432^4*x^7/7 + 12870^4*x^8/8 +...+ A000984(n)^4*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(sum(k=1,n,binomial(2*k,k)^4*x^k/k)+x*O(x^n)),n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A224732, A224734, A224735, A186420, A000984.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Apr 16 2013
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