A144456 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).

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

Offset

1,4

Comments

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

Row sums are:

{1, 0, -3, -60, -2088, -120384, -15959808, -2905846272, -889216828416, -337903021854720, -186522486457466880}.

Links

Table of n, a(n) for n=1..39.

Formula

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)).

Example

{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},

Mathematica

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[%]

Crossrefs

Sequence in context: A109878 A354796 A104565 * A262427 A333986 A349664

Adjacent sequences: A144453 A144454 A144455 * A144457 A144458 A144459

Keyword

uned,sign

Author

Roger L. Bagula and Gary W. Adamson, Oct 07 2008

Status

approved