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

%I A161808 #11 Feb 18 2019 23:47:15
%S A161808 1,3,3,3,9,12,12,27,36,57,141,165,135,321,450,399,780,1068,1308,2913,
%T A161808 3537,2736,5940,8430,7173,13251,18267,17661,35007,45051,31866,58506,
%U A161808 85890,65694,102000,145293,101547,140574,203781,114765,93051,161754
%N A161808 G.f.: A(q) = exp( Sum_{n>=1} A162552(n) * 3*A038500(n) * q^n/n ).
%C A161808 A162552 forms the l.g.f. of log[ Sum_{n>=0} x^(n^2) ], and
%C A161808 A038500(n) is the highest power of 3 dividing n.
%C A161808 The first negative term is a(43) = -162729.
%H A161808 Paul D. Hanna, <a href="/A161808/b161808.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..100 from Georg Fischer)
%e A161808 G.f.: A(q) = 1 + 3*q + 3*q^2 + 3*q^3 + 9*q^4 + 12*q^5 + 12*q^6 +...
%e A161808 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 +...
%e A161808 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 +...
%e A161808 which equals log( Sum_{n>=0} q^(n^2) ) as described by A162552.
%o A161808 (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)}
%Y A161808 Cf. A161804 (variant).
%K A161808 sign
%O A161808 0,2
%A A161808 _Paul D. Hanna_, Jul 21 2009