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A162552 L.g.f.: log( Sum_{n>=0} x^(n^2) ), the log of the characteristic function of the squares.

%I A162552 #8 Jun 22 2023 07:22:07
%S A162552 1,-1,1,3,-4,5,-6,3,10,-16,23,-27,14,6,-34,83,-101,86,-37,-72,204,
%T A162552 -309,346,-243,-29,454,-908,1214,-1130,470,776,-2413,3884,-4421,3244,
%U A162552 162,-5438,11285,-15352,14688,-6887,-8640,29241,-48353,56270,-42850,1834
%N A162552 L.g.f.: log( Sum_{n>=0} x^(n^2) ), the log of the characteristic function of the squares.
%H A162552 Paul D. Hanna, <a href="/A162552/b162552.txt">Table of n, a(n), n = 1..650.</a>
%F A162552 L.g.f.: L(x) = Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=0} x^(n^2) ).
%e A162552 L.g.f.: L(x) = x - 1*x^2/2 + 1*x^3/3 + 3*x^4/4 - 4*x^5/5 + 5*x^6/6 -...
%e A162552 exp(L(x)) = 1 + x + x^4 + x^9 + x^16 + x^25 + x^36 +...+ x^(n^2) +...
%o A162552 (PARI) {a(n)=local(Q=sum(m=0,sqrtint(n+1),x^(m^2))+x*O(x^n));n*polcoeff(log(Q),n)}
%Y A162552 Cf. A162553, A002129, A010052.
%K A162552 sign
%O A162552 1,4
%A A162552 _Paul D. Hanna_, Jul 06 2009