A144455 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}]].

1, -1, 1, -8, 0, 2, -216, -144, -6, 6, -27000, -27000, -8070, -600, 30, -9261000, -10848600, -4402230, -728490, -40530, 210, -12326391000, -15613428600, -7239662430, -1533659820, -148745520, -5271420, 2310, -27081081027000, -36396684324000, -18558752282070, -4600370144370

Offset

1,4

Comments

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

Row sums are:

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

Links

Table of n, a(n) for n=1..32.

Formula

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)).

Example

{1},
{-1, 1},
{-8, 0, 2},
{-216, -144, -6, 6},
{-27000, -27000, -8070, -600,30},
{-9261000, -10848600, -4402230, -728490, -40530, 210},
{-12326391000, -15613428600, -7239662430, -1533659820, -148745520, -5271420, 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 + Prime[i], {i, 1, n - 1}]]; Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A094240 A200093 A179068 * A251866 A300713 A373513

Adjacent sequences: A144452 A144453 A144454 * A144456 A144457 A144458

Keyword

uned,sign

Author

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

Status

approved