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Search: id:A137339
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| A137339 |
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A triangular sequence from a functional coefficient expansion of a raising factorial type: p(x,t)=1/(1-t)^(m*x);m=3. |
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+0
1
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| 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; listen)
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OFFSET
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1,3
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COMMENT
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Row sums are:
{1, 3, 12, 60, 360, 2520, 20160, 181440, 1814400, 19958400, 239500800}
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REFERENCES
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Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 62 - 63
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FORMULA
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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)).
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EXAMPLE
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{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}
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MATHEMATICA
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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]
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CROSSREFS
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Adjacent sequences: A137336 A137337 A137338 this_sequence A137340 A137341 A137342
Sequence in context: A010030 A117940 A099093 this_sequence A132330 A117078 A021333
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 20 2008
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