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%I #5 Apr 12 2013 00:34:22
%S 1,1,3,12,81,1335,49309,3882180,633703214,212061201327,
%T 144669917959584,200541263416077021,563631413420071614333,
%U 3206926569346230863485855,36897315109526505791310840932,857701705296285206387609947414980,40254707002970300021370965171570478599
%N G.f.: exp( Sum_{n>=1} A219331(n^2)*x^n/n ).
%C A219331 is the logarithmic derivative of A006456, where A006456(n) is the number of compositions of n into sums of squares.
%F Logarithmic derivative yields A224607, where A224607(n) = A219331(n^2).
%e G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 81*x^4 + 1335*x^5 + 49309*x^6 +...
%e where
%e log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 269*x^4/4 + 6181*x^5/5 + 286790*x^6/6 +...+ A219331(n^2)*x^n/n +...
%o (PARI) {A219331(n)=n*polcoeff(-log(1-sum(r=1,sqrtint(n+1),x^(r^2)+x*O(x^n))),n)}
%o {a(n)=polcoeff(exp(sum(m=1,n,A219331(m^2)*x^m/m)+x*O(x^n)),n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A224607, A219331, A006456, A224366.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Apr 12 2013
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