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1, 10, -1, 100, -20, 1, 1000, -300, 30, -1, 10000, -4000, 600, -40, 1, 100000, -50000, 10000, -1000, 50, -1, 1000000, -600000, 150000, -20000, 1500, -60, 1, 10000000, -7000000, 2100000, -350000, 35000, -2100, 70
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Rows sum up to A001019 (powers of 9),diagonals to A004189, a generalization of A010892 (the inverse Fibonacci).Ratio of diagonal sums converges to a decimal sequence: A000108 (Catalan numbers), which is the squared difference of sqrt(2) and sqrt(3), or 5-sqrt(24). Ratio between first binomial transform (A054320 and A138288)of A004189, converges to sqrt(2/3).1/(2*sqrt(24)gives A000984 (central binomial coefficients)as a decimal sequence.
Triangle T(n,k), read by rows, given by [10,0,0,0,0,0,0,0,...] DELTA [ -1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 15 2009]
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FORMULA
| Sum_{k, 0<=k<=n}T(n,k)*x^k = (10-x)^n. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 15 2009]
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EXAMPLE
| Triangle begins:
1
10,-1
100,-20,1
1000,-300,30,-1
10000,-4000,600,-40,1
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CROSSREFS
| Cf. A007318, A130595, A038303, A004189, A010892, A001079, A054320, A138288, A041041, A000108
Sequence in context: A206819 A178865 A164881 * A038303 A178870 A075505
Adjacent sequences: A165290 A165291 A165292 * A165294 A165295 A165296
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KEYWORD
| tabl,sign
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AUTHOR
| M. Dols (markdols99(AT)yahoo.com), Sep 13 2009
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