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%I #14 Apr 15 2013 21:43:39
%S 1,1,1,5,6,7,8,13,28,36,45,59,92,134,186,269,375,538,761,1080,1520,
%T 2157,3060,4339,6181,8750,12394,17554,24912,35322,50066,70957,100596,
%U 142665,202278,286790,406520,576347,817142,1158528,1642461,2328536,3301283,4680417,6635688
%N L.g.f.: -log(1 - Sum_{n>=1} x^(n^2)) = Sum_{n>=1} a(n)*x^n/n.
%C Limit a(n)/a(n+1) = 0.705346681379806989636379706393941505260078161512292870... is a real root of 1 = Sum_{n>=1} x^(n^2).
%H Paul D. Hanna, <a href="/A219331/b219331.txt">Table of n, a(n) for n = 1..1000</a>
%F Logarithmic derivative of A006456, where A006456(n) is the number of compositions of n into sums of squares.
%e L.g.f.: L(x) = x + x^2/2 + x^3/3 + 5*x^4/4 + 6*x^5/5 + 7*x^6/6 + 8*x^7/7 + 13*x^8/8 + 28*x^9/9 + 36*x^10/10 +...
%e where
%e exp(L(x)) = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 5*x^7 + 7*x^8 + 11*x^9 + 16*x^10 + 22*x^11 + 30*x^12 +...+ A006456(n)*x^n +...
%e exp(-L(x)) = 1 - x - x^4 - x^9 - x^16 - x^25 - x^36 +...+ -x^(n^2) +...
%o (PARI) {a(n)=n*polcoeff(-log(1-sum(r=1,sqrtint(n+1),x^(r^2)+x*O(x^n))),n)}
%o for(n=1,50,print1(a(n),", "))
%Y Cf. A224607, A224608, A006456.
%K nonn
%O 1,4
%A _Paul D. Hanna_, Apr 12 2013
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