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A122192
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Sum of the n-th powers of the roots of the (reduced) weight enumerator of the extended Golay code (1 + 759*x^2 + 2576*x^3 + 759*x^4 + x^6).
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2
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6, 0, -1518, -7728, 1149126, 9775920, -851127150, -10374206304, 619950551814, 10059106207584, -443172509029998, -9223980220220304, 309985135145332422, 8134978519171135632, -211181377213616588526, -6965969413257227260608, 139095682365347347024902
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: 6*(1 + 506*x^2 + 1288*x^3 + 253*x^4)/(1 + 759*x^2 + 2576*x^3 + 759*x^4 + x^6).
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MAPLE
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Newt:=proc(f) local t1, t2, t3, t4; t1:=f; t2:=diff(f, x); t3:=expand(x^degree(t1, x)*subs(x=1/x, t1)); t4:=expand(x^degree(t2, x)*subs(x=1/x, t2)); factor(t4/t3); end;
g:=1+759*x^2+2576*x^3+759*x^4+x^6; Newt(g); series(%, x, 60);
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MATHEMATICA
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LinearRecurrence[{0, -759, -2576, -759, 0, -1}, {6, 0, -1518, -7728, 1149126, 9775920}, 30] (* G. C. Greubel, Jul 11 2021 *)
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PROG
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(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 6*(1+506*x^2+1288*x^3+253*x^4)/(1+759*x^2+2576*x^3+759*x^4 +x^6) ).list()
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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