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A144456
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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 + 1/Prime[i], {i, 1, n - 1}]]. (Correction to previous submission).
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0
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1, -1, 1, -2, -3, 2, -6, -29, -31, 6, -30, -299, -920, -869, 30, -210, -3569, -21193, -51769, -43853, 210, -2310, -64679, -665252, -3136692, -6760012, -5333173, 2310, -30030, -1231229, -19579519, -153212408, -618042328, -1212020249, -901760539, 30030, -510510, -29609579, -688677932
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OFFSET
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1,4
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COMMENTS
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The name contains an unmatched parenthesis. - Editors, Mar 13 2024
Row sums are:
{1, 0, -3, -60, -2088, -120384, -15959808, -2905846272, -889216828416, -337903021854720, -186522486457466880}.
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LINKS
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FORMULA
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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)).
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EXAMPLE
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{1},
{-1, 1},
{-2, -3, 2},
{-6, -29, -31, 6},
{-30, -299, -920, -869, 30},
{-210, -3569, -21193, -51769, -43853, 210},
{-2310, -64679, -665252, -3136692, -6760012, -5333173, 2310},
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MATHEMATICA
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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[%]
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CROSSREFS
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KEYWORD
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uned,sign
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AUTHOR
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STATUS
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approved
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