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G.f.: exp( Sum_{n>=1} x^n/n * (1 - 3*x^n)/(1 - x^n) ).
1

%I #10 Dec 15 2015 16:54:29

%S 1,1,-1,-3,-4,-2,1,5,8,8,6,2,-4,-10,-13,-15,-14,-10,-3,5,12,18,23,25,

%T 23,17,9,1,-9,-19,-28,-34,-37,-35,-30,-24,-15,-3,10,24,35,43,48,50,50,

%U 46,38,26,12,-4,-20,-34,-45,-55,-64,-70,-71,-67,-58,-46,-31,-15,2,18,35,53,68,80,89,93,91,85,75,63,49,33,15,-7,-31,-53,-72,-88,-101,-109,-114,-114,-111,-105,-96,-82,-63

%N G.f.: exp( Sum_{n>=1} x^n/n * (1 - 3*x^n)/(1 - x^n) ).

%H Paul D. Hanna, <a href="/A264928/b264928.txt">Table of n, a(n) for n = 0..5000</a>

%F G.f.: ( Product_{n>=1} 1 - x^n )^2 / (1-x)^3.

%e G.f.: A(x) = 1 + x - x^2 - 3*x^3 - 4*x^4 - 2*x^5 + x^6 + 5*x^7 + 8*x^8 + 8*x^9 + 6*x^10 + 2*x^11 - 4*x^12 - 10*x^13 - 13*x^14 - 15*x^15 +...

%e where

%e log(A(x)) = x*(1-3*x)/(1-x) + x^2/2*(1-3*x^2)/(1-x^2) + x^3/3*(1-3*x^3)/(1-x^3) + x^4/4*(1-3*x^4)/(1-x^4) + x^5/5*(1-3*x^5)/(1-x^5) +...

%e Also,

%e A(x)*(1-x)^3 = (1-x)^2 * (1-x^2)^2 * (1-x^3)^2 * (1-x^4)^2 * (1-x^5)^3 *...

%o (PARI) {a(n) = my(A=1); A = exp( sum(k=1, n+1, (x^k*(1 - 3*x^k)/(1 - x^k)) /k +x*O(x^n) ) ); polcoeff(A, n)}

%o for(n=0,120,print1(a(n),", "))

%K sign,look

%O 0,4

%A _Paul D. Hanna_, Dec 14 2015