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A123228 Sum of the n-th powers of the roots of the polynomial x^6 + 14x^5 + 87x^4 + 148x^3 + 87x^2 + 14x + 1. 1

%I #5 Jul 20 2016 10:50:02

%S 6,-14,22,466,-6714,51346,-205418,-638414,19787526,-195455054,

%T 1126500502,-1636604654,-47878102074,662684162386,-4965254864618,

%U 19072814136946,71067700116486,-1976406503675534,19086772122105622,-107375947452919214,128777308208472006,4884916184617735186

%N Sum of the n-th powers of the roots of the polynomial x^6 + 14x^5 + 87x^4 + 148x^3 + 87x^2 + 14x + 1.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-13,-74,-74,-13,-1).

%F G.f.: 2*(7*x^4+80*x^3+142*x^2+32*x+3)/((x+1)*(x^4+12*x^3+62*x^2+12*x+1)).

%p 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;

%p t1:=1+14*x+87*x^2+148*x^3+87*x^4+14*x^5+x^6; Newt(t1); series(t1,x,50);

%o (PARI) polsym(x^6 + 14*x^5 + 87*x^4 + 148*x^3 + 87*x^2 + 14*x + 1, 30) \\ _Charles R Greathouse IV_, Jul 20 2016

%Y This polynomial arises in A001496. Cf. A123259.

%K sign,easy

%O 0,1

%A _N. J. A. Sloane_, Nov 12 2006

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Last modified July 25 05:51 EDT 2024. Contains 374586 sequences. (Running on oeis4.)