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A137433 Coefficients of A000930 expansion similar to that given for Fibonacci numbers in Roman's Umbral Calculus. 0
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; text; internal format)
OFFSET

1,8

COMMENTS

Row sums:

{1, 1, 2, 12, 72, 480, 4320, 45360, 524160, 6894720, 101606400}

Row_sum(n)/n!=A000930(n)

REFERENCES

Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 149-150

LINKS

Table of n, a(n) for n=1..55.

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}]

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}

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]

CROSSREFS

Cf. A000045, A000930.

Sequence in context: A200025 A200300 A268440 * A318409 A119278 A070064

Adjacent sequences:  A137430 A137431 A137432 * A137434 A137435 A137436

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 17 2008

STATUS

approved

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Last modified September 17 04:03 EDT 2019. Contains 327119 sequences. (Running on oeis4.)