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%I #6 Mar 13 2024 19:21:28
%S 1,-1,1,-2,-3,2,-6,-29,-31,6,-30,-299,-920,-869,30,-210,-3569,-21193,
%T -51769,-43853,210,-2310,-64679,-665252,-3136692,-6760012,-5333173,
%U 2310,-30030,-1231229,-19579519,-153212408,-618042328,-1212020249,-901760539,30030,-510510,-29609579,-688677932
%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 + 1/Prime[i], {i, 1, n - 1}]]. (Correction to previous submission).
%C The name contains an unmatched parenthesis. - Editors, Mar 13 2024
%C Row sums are:
%C {1, 0, -3, -60, -2088, -120384, -15959808, -2905846272, -889216828416, -337903021854720, -186522486457466880}.
%F a(n)=Prime[n](a(n-1); p(x,n)=If[n == 0, 1, a[n - 1]*(x - a[n - 1])*Product[x + 1/Prime[i], {i, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).
%e {1},
%e {-1, 1},
%e {-2, -3, 2},
%e {-6, -29, -31, 6},
%e {-30, -299, -920, -869, 30},
%e {-210, -3569, -21193, -51769, -43853, 210},
%e {-2310, -64679, -665252, -3136692, -6760012, -5333173, 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 + 1/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
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