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A triangle sequence of coefficients of polynomials with roots that are inverse primes: a(n)=Prime[n](a(n-1); p(x,n)=If[n == 0, 1, a[n - 1]*(x - a[n - 1])*Product[x + Prime[i], {i, 1, n - 1}]].
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%I #8 Mar 13 2024 19:21:40

%S 1,-1,1,-8,0,2,-216,-144,-6,6,-27000,-27000,-8070,-600,30,-9261000,

%T -10848600,-4402230,-728490,-40530,210,-12326391000,-15613428600,

%U -7239662430,-1533659820,-148745520,-5271420,2310,-27081081027000,-36396684324000,-18558752282070,-4600370144370

%N A triangle sequence of coefficients of polynomials with roots that are inverse primes: a(n)=Prime[n](a(n-1); p(x,n)=If[n == 0, 1, a[n - 1]*(x - a[n - 1])*Product[x + Prime[i], {i, 1, n - 1}]].

%C The name contains an unmatched parenthesis. - Editors, Mar 13 2024

%C Row sums are:

%C {1, 0, -6, -360, -62640, -25280640, -36867156480, -87262563548160, -453954083074652160, -3277554562054009036800, -41611836823332419189145600}.

%F a(n)=Prime[n](a(n-1); p(x,n)=If[n == 0, 1, a[n - 1]*(x - a[n - 1])*Product[x + Prime[i], {i, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).

%e {1},

%e {-1, 1},

%e {-8, 0, 2},

%e {-216, -144, -6, 6},

%e {-27000, -27000, -8070, -600,30},

%e {-9261000, -10848600, -4402230, -728490, -40530, 210},

%e {-12326391000, -15613428600, -7239662430, -1533659820, -148745520, -5271420, 2310},

%t a[0] = 1; a[n_] := a[n] = Prime[n]*a[n - 1]; p[x_, n_] := If[n == 0, 1, a[n - 1]*(x - a[n - 1])*Product[x + Prime[i], {i, 1, n - 1}]]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]

%K uned,sign

%O 1,4

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 07 2008