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Search: id:A009998
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| A009998 |
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Triangle in which j-th entry in i-th row is (j+1)^(i-j). |
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+0
14
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| 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 8, 9, 4, 1, 1, 16, 27, 16, 5, 1, 1, 32, 81, 64, 25, 6, 1, 1, 64, 243, 256, 125, 36, 7, 1, 1, 128, 729, 1024, 625, 216, 49, 8, 1, 1, 256, 2187, 4096, 3125, 1296, 343, 64, 9, 1, 1, 512, 6561, 16384, 15625, 7776, 2401, 512, 81, 10, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Read as a square array this is the Hilbert transform of triangle A123125 (see A145905 for the definition of this term). For example, the fourth row of A123125 is (0,1,4,1) and the expansion (x + 4*x^2 + x^3)/(1-x)^4 = x + 8*x^2 + 27*x^3 + 64*x^4 + ... generates the entries in the fourth row of this array read as a square. [From Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008]
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 24.
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LINKS
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T. D. Noe, Rows n=0..50 of triangle, flattened
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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EXAMPLE
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1; 1, 1; 1, 2, 1; 1, 4, 3, 1; 1, 8, 9, 4, 1; 1, 16, 27, 16, 5, 1; 1, 32, 81, 64, 25, 6, 1;...
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CROSSREFS
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Row sums give A026898. Cf. A088956.
A123125. [From Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008]
Sequence in context: A137743 A099239 A167630 this_sequence A113993 A103323 A092056
Adjacent sequences: A009995 A009996 A009997 this_sequence A009999 A010000 A010001
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KEYWORD
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tabl,nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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a(62) corrected to 512 by T. D. Noe, Dec 20 2007
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