login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A173007 A triangle of polynomial coefficients of:q=3; p(x,n,q)=If[n == 0, 1, Product[x + q^i, {i, 1, n}]] 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

Row sums are:

{1, 4, 40, 1120, 91840, 22408960, 16358540800, 35792487270400,

234870301468364800, 4623187014103292723200, 272999193182799435304960000,...}.

a = 2; A108084.

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 (From Philippe Deléham Oct 01 2011).

LINKS

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

FORMULA

q=3;

p(x,n,q)=If[n == 0, 1, Product[x + q^i, {i, 1, n}]]

T(n,k)=3^n*T(n-1,k)+T(n-1,k-1), T(0,0)=1 (From 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},

{22876792454961, 11433166050879, 1427185336941, 54665851779, 674887059, 2685501, 3279, 1},

{150094635296999121, 75035879252272080, 9375196161720780, 360089838858960, 4482599845878, 18294459120, 24199020, 9840, 1},

{2954312706550833698643, 1477081305957768349761, 184607021930402384820, 7097023494422630460, 88591102605275634, 364572438704838, 494603769780, 217879740, 29523, 1},

{174449211009120179071170507, 87223128348206814118735932, 10902337119274288189585941, 419256747344092308417360, 5238313041233343542526, 21616229035687254696, 29570430440444058, 13360184537040, 1961183367, 88572, 1}

MATHEMATICA

Clear[p, x, n, q]

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, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 20:53 EDT 2019. Contains 323534 sequences. (Running on oeis4.)