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%I #5 Apr 27 2019 13:48:55
%S 1,-1,3,-9,28,-74,162,-325,995,-4734,15466,8677,-335037,703456,
%T 10008733,-77798035,-22911395,3588683864,-18537404473,-76218346190,
%U 1450216275105,-4631262043579,-57235991842837,672219894780644,-821654384386424,-40932573680694497,359643851223904326,405144935152085312,-31795393797951609594,220753675876844248793,938030268510143246068,-27834369944198908535526,153463296961588410948143,1346812736734415987235200
%N G.f. A(x) satisfies: Sum_{n>=0} x^n * A(x)^(n^2) = Sum_{n>=0} x^(n^2).
%H Paul D. Hanna, <a href="/A325218/b325218.txt">Table of n, a(n) for n = 0..400</a>
%e G.f.: A(x) = 1 - x + 3*x^2 - 9*x^3 + 28*x^4 - 74*x^5 + 162*x^6 - 325*x^7 + 995*x^8 - 4734*x^9 + 15466*x^10 + 8677*x^11 - 335037*x^12 + 703456*x^13 + 10008733*x^14 - 77798035*x^15 - 22911395*x^16 + 3588683864*x^17 - 18537404473*x^18 - 76218346190*x^19 + 1450216275105*x^20 + ...
%e such that
%e B(x) = 1 + x*A(x) + x^2*A(x)^4 + x^3*A(x)^9 + x^4*A(x)^16 + x^5*A(x)^25 + x^6*A(x)^36 + x^7*A(x)^49 + x^8*A(x)^64 + x^9*A(x)^81 + x^10*A(x)^100 + ...
%e where
%e B(x) = 1 + x + x^4 + x^9 + x^16 + x^25 + x^36 + x^49 + x^64 + x^81 + x^100 + ...
%o (PARI) {a(n) = my(A=[1], SUMSQ = sum(m=0,sqrtint(n+1),x^(m^2)));
%o for(i=1,n, A=concat(A,0); A[#A] = -polcoeff( sum(m=0,#A, x^m*Ser(A)^(m^2) ) - SUMSQ, #A);); H=A; A[n+1]}
%o for(n=0,30,print1(a(n),", "))
%K sign
%O 0,3
%A _Paul D. Hanna_, Apr 27 2019
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