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A246575 Expansion of (Product_{r>=1} (1-x^r))*x^(k^2) / Product_{i=1..k} (1-x^i)^2 with k=1.

%I A246575 #37 Aug 21 2018 08:22:45
%S A246575 0,1,1,0,-1,-2,-2,-2,-1,0,1,2,3,3,3,3,2,1,0,-1,-2,-3,-4,-4,-4,-4,-4,
%T A246575 -3,-2,-1,0,1,2,3,4,5,5,5,5,5,5,4,3,2,1,0,-1,-2,-3,-4,-5,-6,-6,-6,-6,
%U A246575 -6,-6,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,7,7,7,7,7,7,7,6,5,4,3
%N A246575 Expansion of (Product_{r>=1} (1-x^r))*x^(k^2) / Product_{i=1..k} (1-x^i)^2 with k=1.
%H A246575 J. Fulman, <a href="http://dx.doi.org/10.1090/S0273-0979-01-00920-X">Random matrix theory over finite fields</a>, Bull. Amer. Math. Soc., 39 (No. 1, 2002), 51-85, MR1864086 (2002i:60012). See top of page 70, Eq. 1, with k=1.
%F A246575 G.f.: x*exp( Sum_{n>=1} x^n/n * (1 - 2*x^n)/(1 - x^n) ). - _Paul D. Hanna_, Dec 14 2015
%p A246575 fGL:=proc(k) local a,i,r;
%p A246575 a:=x^(k^2)/mul((1-x^i)^2,i=1..k);
%p A246575 a:=a*mul(1-x^r,r=1..101);
%p A246575 series(a,x,101);
%p A246575 seriestolist(%);
%p A246575 end;fGL(1);
%t A246575 nmax = 100; CoefficientList[Series[x*Exp[Sum[x^k/k * (1 - 2*x^k)/(1 - x^k), {k, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Dec 17 2015 *)
%o A246575 (PARI) {a(n) = my(A=1); A = x*exp( sum(k=1, n+1, x^k/k * (1-2*x^k)/(1 - x^k) +x*O(x^n) ) ); polcoeff(A, n)}
%o A246575 for(n=0, 100, print1(a(n), ", ")) \\ _Paul D. Hanna_, Dec 14 2015
%Y A246575 k=0 gives A010815.
%Y A246575 Cf. A246575, A246576, A246577, A246578, A078616.
%K A246575 sign
%O A246575 0,6
%A A246575 _N. J. A. Sloane_, Aug 31 2014