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%I #3 Apr 16 2013 21:50:53
%S 1,8,140,3616,116542,4316080,175593800,7640774080,349626142909,
%T 16632958651688,816163494236860,41069537125459360,2110206360805542510,
%U 110346590629125981872,5857345961837113457864,314962180518584299711424,17128125582951726423704502,940726748732537798295599280
%N G.f.: exp( Sum_{n>=1} binomial(2*n,n)^3 * x^n/n ).
%F Logarithmic derivative yields A002897.
%e G.f.: A(x) = 1 + 8*x + 140*x^2 + 3616*x^3 + 116542*x^4 + 4316080*x^5 +...
%e where
%e log(A(x)) = 2^3*x + 6^3*x^2/2 + 20^3*x^3/3 + 70^3*x^4/4 + 252^3*x^5/5 + 924^3*x^6/6 + 3432^3*x^7/7 + 12870^3*x^8/8 +...+ A000984(n)^3*x^n/n +...
%o (PARI) {a(n)=polcoeff(exp(sum(k=1,n,binomial(2*k,k)^3*x^k/k)+x*O(x^n)),n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A224732, A224734, A224736, A002897, A000984.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Apr 16 2013
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