%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