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 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 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

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