A161803 - OEIS

%I #2 Mar 30 2012 18:37:17

%S 1,2,0,-2,6,12,0,-8,24,44,0,-30,54,104,0,-60,238,466,0,-402,924,1892,

%T 0,-1228,3264,6006,0,-4052,6688,13052,0,-7452,16536,32140,0,-24828,

%U 39660,85744,0,-53592,114336,212406,0,-141090,190754,386956,0,-216572,136078

%N G.f.: A(x) = exp( Sum_{n>=1} A162552(n) * 2*A006519(n) * x^n/n ).

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

%C 2*A006519 forms the l.g.f. of binary partitions (A000123) and

%C A006519(n) is the highest power of 2 dividing n.

%e G.f.: 1 + 2*x - 2*x^3 + 6*x^4 + 12*x^5 - 8*x^7 + 24*x^8 + 44*x^9 +...

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

%Y Cf. A161800, A162552.

%K sign

%O 0,2

%A _Paul D. Hanna_, Jul 19 2009