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A173007 Triangle of polynomial coefficients: p(x,n,q) = 1 if n = 0, Product_{i=1..n} (x + q^i) otherwise, with q = 3. 1
1, 3, 1, 27, 12, 1, 729, 351, 39, 1, 59049, 29160, 3510, 120, 1, 14348907, 7144929, 882090, 32670, 363, 1, 10460353203, 5223002148, 650188539, 24698520, 297297, 1092, 1, 22876792454961, 11433166050879, 1427185336941, 54665851779 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Triangle T(n,k), read by rows, given by [3,6,27,72,243,702,2187,6480,...] DELTA [1,0,3,0,9,0,27,0,81,0,243,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 01 2011

LINKS

Table of n, a(n) for n=0..31.

FORMULA

q=3;

p(x,n,q) = 1 if n=0, Product_{i=1..n} (x + q^i) otherwise.

T(n,k) = 3^n*T(n-1,k) + T(n-1,k-1), T(0,0)=1. - Philippe Deléham, Oct 01 2011

EXAMPLE

{1},

{3, 1},

{27, 12, 1},

{729, 351, 39, 1},

{59049, 29160, 3510, 120, 1},

{14348907, 7144929, 882090, 32670, 363, 1},

{10460353203, 5223002148, 650188539, 24698520, 297297, 1092, 1},

MATHEMATICA

p[x_, n_, q_] = If[n == 0, 1, Product[x + q^i, {i, 1, n}]];

Table[Table[CoefficientList[p[x, n, q], x], {n, 0, 10}], {q, 2, 10}];

Table[Flatten[Table[CoefficientList[p[x, n, q], x], {n, 0, 10}]], {q, 2, 10}]

CROSSREFS

Cf. A108084 (for q=2), A203148.

Sequence in context: A289329 A033464 A170924 * A113099 A317930 A270078

Adjacent sequences:  A173004 A173005 A173006 * A173008 A173009 A173010

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 07 2010

STATUS

approved

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Last modified October 1 11:01 EDT 2020. Contains 337442 sequences. (Running on oeis4.)