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%I #10 May 10 2013 12:45:05
%S 1,1,3,19,214,3846,102206,3795758,188648664,12125977944,980768153832,
%T 97599402813672,11728820086206576,1675575398007779568,
%U 280777781273956353648,54556438705747006028016,12169284368165386948212096,3088938134820388829982311808
%N exp(Sum_{n>0} x^n/n^2) = Sum_{n>=0} a(n)*x^n/n!^2.
%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, second edition, Addison Wesley, pp. 464-466.
%F a(n)=n!^2/n*sum(k=0, n-1, a(k)/k!^2/(n-k)). a(n)/n!^2 = exp(Pi^2/6)/n^2 + O(log(n)/n^3). - _Benoit Cloitre_, Jan 11 2003
%o (PARI) a(n)=if(n<2,1,(n-1)!^2+n!^2/n*sum(k=1,n-1,a(k)/k!^2/(n-k)))
%o (PARI) {a(n)=n!^2*polcoeff(exp(sum(m=1, n, x^m/m^2)+x*O(x^n)), n)}
%Y Cf. A193436, A217145.
%K nonn
%O 0,3
%A _Vladeta Jovovic_, Sep 04 2002
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