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A143228
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Triangle read by rows, T(n,k) = (p(n)*p(k)), where p(n) & p(k) = the number of partitions of n; 0<=k<=n.
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1
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1, 1, 1, 2, 2, 4, 3, 3, 6, 9, 5, 5, 10, 15, 25, 7, 7, 1421, 35, 49, 11, 11, 22, 33, 55, 77, 121, 15, 15, 30, 45, 75, 105, 165, 225, 22, 22, 44, 66, 110, 154, 242, 330, 484, 30, 30, 60, 90, 150, 210, 330, 450, 660, 900, 42, 42, 84, 126, 210, 294, 462630, 924, 1260, 1764
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OFFSET
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0,4
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COMMENTS
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Left border = A000041.
Row sums = A143229: (1, 2, 8, 21, 60, 133, 330, 675,...).
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LINKS
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Table of n, a(n) for n=0..63.
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FORMULA
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Triangle read by rows, T(n,k) = (p(n)*p(k)), where p(n) & p(k) = the number of partitions of n. Let X = the infinite lower triangular matrix with A000041 in the main diagonal and the rest zeros = A000041 * 0^(n-k); 0<=k<=n. The triangle = X * A000012 * X.
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EXAMPLE
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First few rows of the triangle =
1;
1, 1;
2, 2, 4;
3, 3, 6, 9;
5, 5, 10, 15, 25;
7, 7, 14, 21, 35, 49;
11, 11, 22, 33, 55, 77, 121;
15, 15, 30, 45, 75, 105, 165, 225;
...
T(7,4) = 75 = p(7) * p(4) = 15 * 5.
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CROSSREFS
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Cf. A000041, A143229.
Sequence in context: A212652 A205678 A128590 * A143211 A209755 A131052
Adjacent sequences: A143225 A143226 A143227 * A143229 A143230 A143231
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Jul 31 2008
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STATUS
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approved
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