A161808 G.f.: A(q) = exp( Sum_{n>=1} A162552(n) * 3*A038500(n) * q^n/n ).

1, 3, 3, 3, 9, 12, 12, 27, 36, 57, 141, 165, 135, 321, 450, 399, 780, 1068, 1308, 2913, 3537, 2736, 5940, 8430, 7173, 13251, 18267, 17661, 35007, 45051, 31866, 58506, 85890, 65694, 102000, 145293, 101547, 140574, 203781, 114765, 93051, 161754

Offset: 0

Author

Paul D. Hanna, Jul 21 2009

Keywords

• sign

Comments

A162552 forms the l.g.f. of log[ Sum_{n>=0} x^(n^2) ], and

A038500(n) is the highest power of 3 dividing n.

The first negative term is a(43) = -162729.

Examples

			G.f.: A(q) = 1 + 3*q + 3*q^2 + 3*q^3 + 9*q^4 + 12*q^5 + 12*q^6 +...
log(A(q)) = 3*q - 3*q^2/2 + 9*q^3/3 + 9*q^4/4 - 12*q^5/5 + 45*q^6/6 - 18*q^7/7 +...
Compare to: q - q^2/2 + q^3/3 + 3*q^4/4 - 4*q^5/5 + 5*q^6/6 - 6*q^7/7 +...
which equals log( Sum_{n>=0} q^(n^2) ) as described by A162552.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..10000 (terms 0..100 from Georg Fischer)

Crossrefs

Cf. A161804 (variant).

Programs

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)*3*3^valuation(k,3)*x^k)+x*O(x^n));polcoeff(A,n)}