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

1, -1, 1, 3, -4, 5, -6, 3, 10, -16, 23, -27, 14, 6, -34, 83, -101, 86, -37, -72, 204, -309, 346, -243, -29, 454, -908, 1214, -1130, 470, 776, -2413, 3884, -4421, 3244, 162, -5438, 11285, -15352, 14688, -6887, -8640, 29241, -48353, 56270, -42850, 1834

Offset: 1

Author

Paul D. Hanna, Jul 06 2009

Keywords

• sign

Examples

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

Links

• Paul D. Hanna, Table of n, a(n), n = 1..650.

Crossrefs

Cf. A162553, A002129, A010052.

Programs

PARI

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

Formula

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