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A122753
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A Bezier transform applied to Stirling numbers of the second kind to produce a new triangular array similar to A088996 for Stirling numbers of the first kind.
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1
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1, 0, 1, 0, 1, 0, 1, 1, -1, 0, 1, 4, -5, 1, 0, 1, 11, -14, 1, 2, 0, 1, 26, -24, -29, 36, -9, 0, 1, 57, 1, -244, 281, -104, 9, 0, 1, 120, 225, -1259, 1401, -454, -83, 50, 0, 1, 247, 1268, -5081, 4621, 911, -3422, 1723, -267, 0, 1, 502, 5278, -16981, 5335, 30871, -44260, 24739, -5897, 413
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,12
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COMMENTS
| The similarity of the Steinbach polynomials/ triangular array to Stirling numbers made me realize that the Bezier transform would work on Stirling numbers as well. A088996 comes up from a Bezier transform of Stirling numbers of the first kind similar to this.
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REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, pp. 824-825.
Eric Weisstein's World of Mathematics, "Stirling Number of the Second Kind." http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html
Peter Steinbach, "Golden Fields: A Case for the Heptagon", Mathematics Magazine, Vol. 70, No. 1, Feb. 1997.
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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FORMULA
| T(n,m)=StirlingS2[m, n] Bezier transform: T'(n,m)=CoefficientList[Sum[StirlingS2[m, n]*x^n*(1 - x)^(m - n), {n, 0, m}], x]
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EXAMPLE
| 1
0, 1
0, 1
0, 1, 1,-1
0, 1, 4,-5, 1
0, 1, 11, -14, 1, 2
0, 1, 26, -24, -29, 36, -9
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MATHEMATICA
| a = Table[CoefficientList[Sum[StirlingS2[m, n]*x^n*(1 - x)^(m - n), {n, 0, m}], x], {m, 0, 10}]; Flatten[a]
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CROSSREFS
| Cf. A088996, A122610.
Sequence in context: A132022 A200013 A178219 * A016714 A113950 A121906
Adjacent sequences: A122750 A122751 A122752 * A122754 A122755 A122756
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 21 2006
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