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%I #6 Dec 03 2018 21:42:32
%S 1,0,0,-2,-2,-2,0,2,2,4,-2,2,0,4,-2,4,6,4,4,-2,-10,-12,-12,-16,-14,6,
%T 6,-4,16,22,30,12,18,-60,-18,-34,-64,-56,-36,-46,16,46,64,70,110,192,
%U 152,124,58,78,-26,-54,-366,-278,-182,-282,-190,40,-112,234,300,476,488,906,732,616,706,154,228,-180,-864,-1112,-1744,-2294,-2824,-3154,-2170,-2146,-2524,-1102,-476,-126,1986,4338,3344,3608,6316,5136,6638,6726,5254,3982,2916,-1466,-86,-6710,-6502,-9900,-9128,-14170,-12232,-13940,-9192,-6892,-6270,3762,7058,9468,23860,22556,29812,40150,34952,30350
%N a(n) = coefficient of x^n*y^n in Product_{n>=1} (1 - (x^n + y^n)).
%H Paul D. Hanna, <a href="/A322213/b322213.txt">Table of n, a(n) for n = 0..500</a>
%e G.f.: A(x) = 1 - 2*x^3 - 2*x^4 - 2*x^5 + 2*x^7 + 2*x^8 + 4*x^9 - 2*x^10 + 2*x^11 + 4*x^13 - 2*x^14 + 4*x^15 + 6*x^16 + 4*x^17 + 4*x^18 - 2*x^19 - 10*x^20 + ...
%e RELATED SERIES.
%e The product P(x,y) = Product_{n>=1} (1 - (x^n + y^n)) begins
%e P(x,y) = 1 + (-1*x - 1*y) + (-1*x^2 + 0*x*y - 1*y^2) + (0*x^3 + 1*x^2*y + 1*x*y^2 + 0*y^3) + (0*x^4 + 1*x^3*y + 0*x^2*y^2 + 1*x*y^3 + 0*y^4) + (1*x^5 + 1*x^4*y + 1*x^3*y^2 + 1*x^2*y^3 + 1*x*y^4 + 1*y^5) + (0*x^6 + 0*x^5*y + 0*x^4*y^2 - 2*x^3*y^3 + 0*x^2*y^4 + 0*x*y^5 + 0*y^6) + (1*x^7 + 0*x^6*y + 0*x^5*y^2 + 0*x^4*y^3 + 0*x^3*y^4 + 0*x^2*y^5 + 0*x*y^6 + 1*y^7) + (0*x^8 - 1*x^7*y + 0*x^6*y^2 - 1*x^5*y^3 - 2*x^4*y^4 - 1*x^3*y^5 + 0*x^2*y^6 - 1*x*y^7 + 0*y^8) + (0*x^9 - 1*x^8*y - 1*x^7*y^2 - 2*x^6*y^3 - 1*x^5*y^4 - 1*x^4*y^5 - 2*x^3*y^6 - 1*x^2*y^7 - 1*x*y^8 + 0*y^9) + (0*x^10 - 1*x^9*y + 0*x^8*y^2 + 0*x^7*y^3 + 1*x^6*y^4 - 2*x^5*y^5 + 1*x^4*y^6 + 0*x^3*y^7 + 0*x^2*y^8 - 1*x*y^9 + 0*y^10) + (0*x^11 - 1*x^10*y - 1*x^9*y^2 + 0*x^8*y^3 - 1*x^7*y^4 + 0*x^6*y^5 + 0*x^5*y^6 - 1*x^4*y^7 + 0*x^3*y^8 - 1*x^2*y^9 - 1*x*y^10 + 0*y^11) + (-1*x^12 - 1*x^11*y + 0*x^10*y^2 + 0*x^9*y^3 - 1*x^8*y^4 + 0*x^7*y^5 + 0*x^6*y^6 + 0*x^5*y^7 - 1*x^4*y^8 + 0*x^3*y^9 + 0*x^2*y^10 - 1*x*y^11 - 1*y^12) + ...
%e in which this sequence equals the coefficients of x^n*y^n for n >= 0.
%o (PARI)
%o {P = prod(n=1, 121, (1 - (x^n + y^n) +O(x^121) +O(y^121)) ); }
%o {a(n) = polcoeff( polcoeff( P, n, x), n, y)}
%o for(n=0, 120, print1( a(n), ", ") )
%Y Cf. A322211.
%K sign
%O 0,4
%A _Paul D. Hanna_, Dec 03 2018
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