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A123319
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Recursive polynomial for A008275 shifted up one value of k: p(k,x)=(-x + k + 1)*p(k - 1, x) This triangular sequence:p(0, x) = 1; p(1, x] = -x + 1; A008275: p(-1, x) = 1; p(0, x] = -x + 1;.
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4
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1, 1, -1, 3, -4, 1, 12, -19, 8, -1, 60, -107, 59, -13, 1, 360, -702, 461, -137, 19, -1, 2520, -5274, 3929, -1420, 270, -26, 1, 20160, -44712, 36706, -15289, 3580, -478, 34, -1, 181440, -422568, 375066, -174307, 47509, -7882, 784, -43, 1, 1814400, -4407120, 4173228, -2118136, 649397, -126329, 15722
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Shifting initial condition in a recurvise polynomial without changing also the function of the interation variable k produces a new triangular sequence. The result here is a variation of Stirling's numbers of the first kind. The Chang and Sederberg version of this recursion produces an even function in sections.
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REFERENCES
| Over and Over Again, Chang and Sederberg,MAA,1997, page 209 ( Moving Averages)
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FORMULA
| p(k,x)=(-x + k + 1)*p(k - 1, x) This triangular sequence:p(0, x) = 1; p(1, x] = -x + 1;
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EXAMPLE
| Triangular sequence:
{1},
{1, -1},
{3, -4, 1},
{12, -19, 8, -1},
{60, -107, 59, -13, 1},
{360, -702, 461, -137, 19, -1},
{2520, -5274, 3929, -1420, 270, -26, 1}
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MATHEMATICA
| p[0, x] = 1; p[1, x] = -x + 1; p[k_, x_] := p[k, x] = (-x + k + 1)*p[k - 1, x]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
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CROSSREFS
| Cf. A008275.
Sequence in context: A114608 A154602 A109956 * A076785 A110506 A114189
Adjacent sequences: A123316 A123317 A123318 * A123320 A123321 A123322
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KEYWORD
| sign,uned,tabl
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Nov 09 2006
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EXTENSIONS
| Offset corrected to 0. - Wolfdieter Lang, Oct 25 2011.
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