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%I #6 Jun 14 2018 08:43:43
%S 1,-1,-2,10,-25,33,57,-561,2310,-7150,18448,-39168,55114,41990,
%T -726750,3657006,-13846041,44907185,-130605450,347227650,-845335695,
%U 1842623895,-3311675445,3271798125,9143639100,-77910795756,356581496251,-1331363100907,4430526577054,-13595755404934,39119816049161,-106498829726801,275433122695473,-676162020887697,1563087628000497,-3329539580829865,6175049600047825
%N G.f. A(x) satisfies: [x^k] (1+x)^(n^2) * A(x) = 0 for k = (n-1)^2 + 1 through k = n^2 for n >= 1.
%H Paul D. Hanna, <a href="/A305600/b305600.txt">Table of n, a(n) for n = 0..2500</a>
%o (PARI) /* Informal code to generate terms */
%o {A=[1,-1]; for(i=1,400, A=concat(A,0); m=sqrtint(#A-2)+1; A[#A] = -polcoeff( (1+x +x*O(x^#A))^(m^2)*Ser(A),#A-1) ;print1(#A,","));A}
%o /* Show that the definition is satisfied: */
%o for(n=1,sqrtint(#A),print1(n": ");for(k=(n-1)^2+1,n^2,print1(polcoeff( (1+x+x*O(x^#A))^(n^2)*Ser(A) ,k),","));print(""))
%K sign
%O 0,3
%A _Paul D. Hanna_, Jun 13 2018
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