|
Search: id:A137432
|
|
|
| A137432 |
|
Coefficients of Fibonacci numbers expansion given in Roman's Umbral Calculus. |
|
+0
1
|
|
| 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)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
Row sums: {1, 1, 4, 18, 120, 960, 9360, 105840, 1370880, 19958400, 322963200}
Row_sum(n)/n!=A000045
|
|
REFERENCES
|
Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 149-150
|
|
FORMULA
|
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}]
|
|
EXAMPLE
|
{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}
|
|
MATHEMATICA
|
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]
|
|
CROSSREFS
|
Cf. A000045.
Sequence in context: A103685 A162971 A078521 this_sequence A135871 A126178 A094753
Adjacent sequences: A137429 A137430 A137431 this_sequence A137433 A137434 A137435
|
|
KEYWORD
|
nonn,tabl,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 17 2008
|
|
|
Search completed in 0.002 seconds
|
