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Search: id:A137431
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| A137431 |
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Coefficients of tribonacci numbers expansion : similar to the Fibonacci number expansion given in Steve Roman's Umbral Calculus. |
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+0
1
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| 1, 0, 1, 0, 3, 1, 0, 14, 9, 1, 0, 66, 83, 18, 1, 0, 504, 750, 275, 30, 1, 0, 4680, 7954, 3915, 685, 45, 1, 0, 51120, 96852, 58324, 13965, 1435, 63, 1, 0, 660240, 1349676, 933156, 280609, 39480, 2674, 84, 1, 0, 9717120, 21158064, 16282412, 5781132, 1030449
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums:
{1, 1, 4, 24, 168, 1560, 17280, 221760, 3265920, 54069120, 994291200}
Row_sum(n)/n!=A000073
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REFERENCES
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Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 149-150
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FORMULA
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Coefficients expansion of p(x,n) in f(x,t)=1/(1-t-t^2-t^3)^x=Sum[p(x,n)*t^n/n!m{n,1,Infinity}].
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EXAMPLE
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{1},
{0, 1},
{0, 3, 1},
{0, 14, 9, 1},
{0, 66, 83, 18, 1},
{0, 504, 750, 275, 30, 1},
{0, 4680, 7954, 3915, 685, 45, 1},
{0, 51120, 96852, 58324, 13965, 1435, 63, 1}, {0, 660240, 1349676, 933156, 280609, 39480, 2674, 84, 1},
{0, 9717120, 21158064, 16282412, 5781132, 1030449, 95256, 4578, 108, 1},
{0, 160755840, 369056016, 309496500, 124949600, 26688375, 3132633, 204750, 7350, 135, 1}
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MATHEMATICA
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Clear[p, g]; p[t_] = 1/(1 - t - t^2-t^3)^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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Cf. A000045, A000073.
Sequence in context: A094753 A143398 A067176 this_sequence A131222 A114151 A147723
Adjacent sequences: A137428 A137429 A137430 this_sequence A137432 A137433 A137434
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 17 2008
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