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Search: id:A123202
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| A123202 |
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Triangular array formed from the coefficients of the Bezier transform of AO21009(n,m): t(n,m,x)=A021009(n,m)*x^m*(1 - x)^(n - m). |
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1
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| 1, 1, -2, 2, -8, 7, 6, -36, 63, -34, 24, -192, 504, -544, 209, 120, -1200, 4200, -6800, 5225, -1546, 720, -8640, 37800, -81600, 94050, -55656, 13327, 5040, -70560, 370440, -999600, 1536150, -1363572, 653023, -130922, 40320, -645120, 3951360, -12794880, 24578400, -29089536, 20896736, -8379008
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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Abramowitz and Stegun, Handbook of Mathematical Functions,9th printing,1972, page 782
Chang and Sederberg, Over and Over Again, MAA, 1997, page 164, figure 26.1.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
Eric Weisstein's World of Mathematics, LaguerrePolynomial
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FORMULA
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Coefficient list of: t(n,m,x)=A021009(n,m)*x^m*(1 - x)^(n - m)
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EXAMPLE
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1
1, 2
2, -8, 7
6, -36, 63, -34
24, -192, 504, -544, 209
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MATHEMATICA
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w = Table[n!*CoefficientList[LaguerreL[n, x], x], {n, 0, 10}]; v = Table[CoefficientList[Sum[w[[n + 1]][[m + 1]]*x^ m*(1 - x)^(n - m), {m, 0, n}], x], {n, 0, 10}]; Flatten[v]
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CROSSREFS
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Cf. A021009.
Adjacent sequences: A123199 A123200 A123201 this_sequence A123203 A123204 A123205
Sequence in context: A067436 A071418 A064862 this_sequence A095297 A094887 A021441
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KEYWORD
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sign
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 04 2006
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EXTENSIONS
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Edited by njas, Jun 12 2007
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