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A136457
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Triangle read by rows: coefficients of polynomials defined by recursion p(x,n)=(x-Gamma(n))*p(x,n-1).
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0
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1, -1, 1, 1, -2, 1, -2, 5, -4, 1, 12, -32, 29, -10, 1, -288, 780, -728, 269, -34, 1, 34560, -93888, 88140, -33008, 4349, -154, 1, -24883200, 67633920, -63554688, 23853900, -3164288, 115229, -874, 1, 125411328000, -340899840000, 320383261440, -120287210688, 15971865420, -583918448, 4520189
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| These are inspired by Cornelius-Schultz matrices.
Row sums are: {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...}
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REFERENCES
| E. F. Cornnelius and Phill Shultz, Amer. Math. Monthly, No. 2, 2008.
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FORMULA
| p(x,0)=1; p(x,1)=x-1; p(x,n)=(x-Gamma(n))*p(x,n-1)
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EXAMPLE
| Triangle begins:
{1},
{-1, 1},
{1, -2, 1},
{-2, 5, -4, 1},
{12, -32, 29, -10, 1},
{-288, 780, -728, 269, -34, 1},
{34560, -93888, 88140, -33008, 4349, -154, 1}
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MATHEMATICA
| Clear[p, x, n, a] p[x, 0] = 1; p[x, 1] = x - 1; p[x_, m_] := p[x, n] = (x - Gamma[n])*p[x, n - 1]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[p[x, n], x]], {n, 0, 10}]; Table[ExpandAll[p[x, n]], {n, 0, 10}];
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CROSSREFS
| Sequence in context: A104560 A121435 A137156 * A078016 A078046 A084600
Adjacent sequences: A136454 A136455 A136456 * A136458 A136459 A136460
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KEYWORD
| tabl,sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 20 2008
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 10 2008
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