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Search: id:A137432
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| A137432 |
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Coefficients of Fibonacci numbers expansion given in Roman's Umbral Calculus. |
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+0
1
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| 1, 0, 1, 0, 3, 1, 0, 8, 9, 1, 0, 42, 59, 18, 1, 0, 264, 450, 215, 30, 1, 0, 2160, 4114, 2475, 565, 45, 1, 0, 20880, 43512, 30814, 9345, 1225, 63, 1, 0, 236880, 528492, 420756, 154609, 27720, 2338, 84, 1, 0, 3064320, 7235568, 6316316, 2673972, 594489, 69552
(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, 18, 120, 960, 9360, 105840, 1370880, 19958400, 322963200}
Row_sum(n)/n!=A000045
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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)^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, 8, 9, 1},
{0, 42, 59, 18, 1},
{0, 264, 450, 215, 30, 1},
{0, 2160, 4114, 2475, 565, 45, 1},
{0, 20880, 43512, 30814, 9345, 1225, 63, 1},
{0, 236880, 528492, 420756, 154609, 27720, 2338, 84, 1},
{0, 3064320, 7235568, 6316316, 2673972, 594489, 69552, 4074, 108, 1},
{0, 44634240, 110499696, 103889700, 49087520, 12803175, 1887753, 154350, 6630, 135, 1}
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MATHEMATICA
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Clear[p, g]; p[t_] = 1/(1 - t - t^2)^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.
Sequence in context: A052420 A103685 A078521 this_sequence A135871 A126178 A094753
Adjacent sequences: A137429 A137430 A137431 this_sequence A137433 A137434 A137435
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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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