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 A137339 A triangular sequence from a functional coefficient expansion of a raising factorial type: p(x,t)=1/(1-t)^(m*x);m=3. 0
 1, 0, 3, 0, 3, 9, 0, 6, 27, 27, 0, 18, 99, 162, 81, 0, 72, 450, 945, 810, 243, 0, 360, 2466, 6075, 6885, 3645, 729, 0, 2160, 15876, 43848, 59535, 42525, 15309, 2187, 0, 15120, 117612, 354564, 548289, 476280, 234738, 61236, 6561, 0, 120960, 986256, 3189348 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row sums are: {1, 3, 12, 60, 360, 2520, 20160, 181440, 1814400, 19958400, 239500800} Also the Bell transform of A052560. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 27 2016 REFERENCES Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 62 - 63 LINKS FORMULA p(x,t)=1/(1-t)^(m*x)=Sum[s(x,n)*t^n/n!;m=3. out_n,m=n!*Coefficients( s(x,n)). EXAMPLE {1}, {0, 3}, {0, 3, 9}, {0, 6, 27, 27}, {0, 18, 99, 162, 81}, {0, 72, 450, 945, 810, 243}, {0, 360, 2466, 6075, 6885, 3645, 729}, {0, 2160, 15876, 43848, 59535, 42525, 15309, 2187}, {0, 15120, 117612, 354564, 548289, 476280, 234738, 61236, 6561}, {0, 120960, 986256, 3189348, 5450004, 5455107, 3306744, 1194102, 236196, 19683}, {0, 1088640, 9239184, 31662900, 58618080, 65445975, 46126017, 20667150, 5708070, 885735, 59049} MAPLE # The function BellMatrix is defined in A264428. BellMatrix(n -> 3*n!, 8); # Peter Luschny, Jan 27 2016 MATHEMATICA Clear[p, g, m]; m = 3; p[t_] = 1/(1 - t)^(m*x); Table[ ExpandAll[n!SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a] (* Second program: *) BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]]; B = BellMatrix[3#!&, rows = 12]; Table[B[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 28 2018, after Peter Luschny *) CROSSREFS Sequence in context: A197270 A117940 A099093 * A230184 A132330 A117078 Adjacent sequences:  A137336 A137337 A137338 * A137340 A137341 A137342 KEYWORD nonn,uned,tabl AUTHOR Roger L. Bagula, Apr 20 2008 STATUS approved

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Last modified October 23 06:13 EDT 2018. Contains 316519 sequences. (Running on oeis4.)