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A137433
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Coefficients of A000930 expansion similar to that given for Fibonacci numbers in Roman's Umbral Calculus.
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0
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1, 0, 1, 0, 1, 1, 0, 8, 3, 1, 0, 30, 35, 6, 1, 0, 144, 230, 95, 10, 1, 0, 1200, 1954, 945, 205, 15, 1, 0, 10800, 19824, 11494, 2835, 385, 21, 1, 0, 105840, 216012, 149212, 45409, 7000, 658, 28, 1, 0, 1249920, 2692080, 2055500, 740124, 140889, 15120, 1050, 36, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| Row sums:
{1, 1, 2, 12, 72, 480, 4320, 45360, 524160, 6894720, 101606400}
Row_sum(n)/n!=A000930(n)
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REFERENCES
| Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 149-150
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FORMULA
| Coefficients expansion of p(x,n) in f(x,t)=1/(1-t-t^3)^x=Sum[p(x,n)*t^n/n!m{n,1,Infinity}]
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EXAMPLE
| {1},
{0, 1},
{0, 1, 1},
{0, 8, 3, 1},
{0, 30, 35, 6, 1},
{0, 144, 230, 95, 10, 1},
{0, 1200, 1954, 945, 205, 15, 1},
{0, 10800, 19824, 11494, 2835, 385, 21, 1},
{0, 105840, 216012, 149212, 45409, 7000, 658, 28, 1},
{0, 1249920, 2692080, 2055500, 740124, 140889, 15120, 1050, 36, 1},
{0, 16692480, 37802736, 31266540, 12628160, 2814525, 370713, 29610, 1590, 45, 1}
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MATHEMATICA
| Clear[p, g]; p[t_] = 1/(1 - t - 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
| Cf. A000045, A000930.
Sequence in context: A010521 A200025 A200300 * A119278 A081822 A070064
Adjacent sequences: A137430 A137431 A137432 * A137434 A137435 A137436
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 17 2008
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