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A124756
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Inverse binomial sum of compositions in standard order.
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2
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0, 1, 2, 0, 3, 1, -1, 0, 4, 2, 0, 1, -2, -2, 1, 0, 5, 3, 1, 2, -1, -1, 2, 1, -3, -4, -1, -3, 2, 3, -1, 0, 6, 4, 2, 3, 0, 0, 3, 2, -2, -3, 0, -2, 3, 4, 0, 1, -4, -6, -3, -6, 0, 0, -4, -4, 3, 6, 2, 6, -2, -4, 1, 0, 7, 5, 3, 4, 1, 1, 4, 3, -1, -2, 1, -1, 4, 5, 1, 2, -3, -5, -2, -5, 1, 1, -3, -3, 4, 7, 3, 7, -1, -3, 2, 1, -5, -8, -5, -9, -2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The standard order of compositions is given by A066099.
This is the final term of the inverse binomial transform of the composition.
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FORMULA
| For a composition b(1),...,b(k), a(n) = Sum_{i=1}^k (-1)^{i-1} C(k-1,i-1) b(i).
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EXAMPLE
| Composition number 11 is 2,1,1; 1*2-2*1+1*1 = 1, so a(11) = 1.
The table starts:
0
1
2 0
3 1 -1 0
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CROSSREFS
| Cf. A066099, A124754, A124755, A011782 (row lengths), A001477 (row sums).
Sequence in context: A168020 A170942 A002187 * A113504 A124754 A047983
Adjacent sequences: A124753 A124754 A124755 * A124757 A124758 A124759
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KEYWORD
| easy,sign,tabf
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AUTHOR
| Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006
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