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A145975
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Triangle read by rows, partition triangle A027293 convolved with A010815.
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3
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1, 1, -1, 2, -1, -1, 3, -2, -1, 0, 5, -3, -2, 0, 0, 7, -5, -3, 0, 0, 1, 11, -7, -5, 0, 0, 1, 0, 15, -11, -7, 0, 0, 2, 0, 1, 22, -15, -11, 0, 0, 3, 0, 1, 0, 30, -22, -15, 0, 0, 5, 0, 2, 0, 42, -30, -22, 0, 0, 7, 0, 3, 0, 0, 0, 56, -42, -30, 0, 0, 11, 0, 5, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Row sums = [1, 0, 0, 0,...]. (a set of matrix operations equivalent to the comment in A010815 that "convolved with the partition numbers = [1, 0, 0, 0,...].
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FORMULA
| Triangle read by rows, = (A027293 * (A010815 * 0^(n-k)); 0<=k<=n. A027293 = an infinite lower triangular matrix with A000041 in every column (the partition numbers). A010815 = (1, -1, -1, 0, 0, 1,...)
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EXAMPLE
| First few rows of the triangle =
1;
1, -1;
2, -1, -1;
3, -2, -1, 0;
5, -3, -2, 0, 0;
7, -5, -3, 0, 0, 1;
11, -7, -5, 0, 0, 1, 0;
15, -11, -7, 0, 0, 2, 0, 1;
22, -15, -11, 0, 0, 3, 0, 1, 0;
30, -22, -15, 0, 0, 5, 0, 2, 0, 0;
42, -30, -22, 0, 0, 7, 0, 3, 0, 0, 0;
...
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CROSSREFS
| A027293, Cf. A010815, A000041
Sequence in context: A127948 A177350 A190688 * A026792 A139100 A036037
Adjacent sequences: A145972 A145973 A145974 * A145976 A145977 A145978
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KEYWORD
| tabl,sign
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 25 2008
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