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A162420 G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*|A002129(n)|*x^n/n ).

%I A162420 #2 Mar 30 2012 18:37:17
%S A162420 1,1,2,7,16,28,57,118,238,432,792,1491,2759,4836,8522,15126,26419,
%T A162420 45114,76883,130792,220578,367144,608252,1005102,1649904,2684354,
%U A162420 4349068,7022762,11278628,18002603,28621347,45345249,71528789,112295812
%N A162420 G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*|A002129(n)|*x^n/n ).
%C A162420 A002129 forms the l.g.f. of log[ Sum_{n>=0} x^(n(n+1)/2) ], while
%C A162420 A000203 forms the l.g.f. of log[ 1/eta(x) ]
%C A162420 where eta(x)^3 = Sum_{n>=0} (-1)^n*(2n+1)*x^(n(n+1)/2).
%F A162420 G.f.: A(x) = exp( L(x) ) where L(x) is the l.g.f. of A162419.
%e A162420 G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 16*x^4 + 28*x^5 + 57*x^6 +...
%e A162420 log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 35*x^4/4 + 36*x^5/5 + 48*x^6/6 +...
%e A162420 where log(A(x)) is the l.g.f. of A162419 and
%e A162420 log(A(x)) = 1*1*x + 3*1*x^2/2 + 4*4*x^3/3 + 7*5*x^4/4 + 6*6*x^5/5 +...
%e A162420 is formed from the term-wise product of the (unsigned) sequences:
%e A162420 A000203:[1, 3,4, 7,6,12,8, 15,13,18,12, 28,14,24,24, 31,18,...];
%e A162420 A002129:[1,-1,4,-5,6,-4,8,-13,13,-6,12,-20,14,-8,24,-29,18,...].
%o A162420 (PARI) {a(n)=local(L=sum(m=1,n,sigma(m)*sumdiv(m, d, (-1)^(m-d)*d)*x^m/m)+x*O(x^n)); polcoeff(exp(L),n)}
%Y A162420 Cf. A162419, A000203, A002129.
%K A162420 nonn
%O A162420 0,3
%A A162420 _Paul D. Hanna_, Jul 03 2009