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%I #4 Mar 30 2012 18:37:17
%S 1,1,1,1,3,6,10,15,18,35,73,143,230,296,416,753,1673,2934,4203,5654,
%T 9135,17881,33102,52787,73749,107869,189629,359107,619296,923833,
%U 1306855,2065717,3776424,6823452,10935160,15822727,23395694,39675378
%N G.f.: A(x) = exp( Sum_{n>=1} A162552(n)^2*x^n/n ) where the l.g.f. of A162552 is the log of the characteristic function of the squares.
%C A162552 is defined by: exp( Sum_{n>=1} A162552(n)*x^n/n ) = Sum_{n>=0} x^(n^2).
%H Paul D. Hanna, <a href="/A162553/b162553.txt">Table of n, a(n), n = 0..330.</a>
%e G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 6*x^4 + 10*x^5 + 15*x^6 +...
%e log(A(x)) = x + x^2/2 + x^3/3 + 9*x^4/4 + 16*x^5/5 + 25*x^6/6 + 36*x^7/7 +...+ A162552(n)^2*x^n/n +...
%e Let L(x) = x - 1*x^2/2 + 1*x^3/3 + 3*x^4/4 - 4*x^5/5 + 5*x^6/6 - 6*x^7/7 +...+ A162552(n)*x^n/n +... then
%e exp(L(x)) = 1 + x + x^4 + x^9 + x^16 + x^25 + x^36 +...+ x^(n^2) +...
%e is the characteristic function of the squares (A010052).
%o (PARI) {a(n)=local(Q=sum(m=0,n,x^(m^2))+x*O(x^n),A); A=exp(sum(k=1,n,polcoeff(log(Q),k)^2*k*x^k)+x*O(x^n));polcoeff(A,n)}
%Y Cf. A162552, A010052, A162416 (variant).
%K nonn
%O 0,5
%A _Paul D. Hanna_, Jul 06 2009
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