A162552 - OEIS

%I #8 Jun 22 2023 07:22:07

%S 1,-1,1,3,-4,5,-6,3,10,-16,23,-27,14,6,-34,83,-101,86,-37,-72,204,

%T -309,346,-243,-29,454,-908,1214,-1130,470,776,-2413,3884,-4421,3244,

%U 162,-5438,11285,-15352,14688,-6887,-8640,29241,-48353,56270,-42850,1834

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

%H Paul D. Hanna, <a href="/A162552/b162552.txt">Table of n, a(n), n = 1..650.</a>

%F L.g.f.: L(x) = Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=0} x^(n^2) ).

%e 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 exp(L(x)) = 1 + x + x^4 + x^9 + x^16 + x^25 + x^36 +...+ x^(n^2) +...

%o (PARI) {a(n)=local(Q=sum(m=0,sqrtint(n+1),x^(m^2))+x*O(x^n));n*polcoeff(log(Q),n)}

%Y Cf. A162553, A002129, A010052.

%K sign

%O 1,4

%A _Paul D. Hanna_, Jul 06 2009