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A038303
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Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*1^j.
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4
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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, 1, 100000000, 80000000, 28000000
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| T(i,j) is the number of i-permutations of 11 objects a,b,c,d,e,f,g,h,i,j,k, with repetition allowed, containing j a's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 21 2007
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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REFERENCES
| B. N. Cyvin et al., Isomer enumeration of unbranched catacondensed polygonal systems with pentagons and heptagons, Match, No. 34 (Oct 1996), pp. 109-121.
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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
| 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, 1
100000000, 80000000, 28000000, 5600000, 700000, 56000, 2800, 80, 1
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MAPLE
| for i from 0 to 8 do seq(binomial(i, j)*10^(i-j), j = 0 .. i) od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 21 2007
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CROSSREFS
| Sequence in context: A178865 A164881 A165293 * A178870 A075505 A130310
Adjacent sequences: A038300 A038301 A038302 * A038304 A038305 A038306
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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