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A153206
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Convolution triangle by rows, T(n,k) = A153197(n-k) * A153198
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1
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1, 1, 1, 2, 1, 2, 5, 2, 2, 5, 15, 5, 4, 5, 14, 51, 15, 10, 10, 14, 43, 189, 51, 30, 25, 28, 43, 143, 748, 189, 102, 75, 70, 86, 143, 509, 3128, 748, 378, 255, 210, 215, 286, 509, 1922, 13731, 3128, 1496, 945, 714, 645, 715, 1018, 1922, 7651
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OFFSET
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0,4
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COMMENTS
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A153197 prefaced with a 1: (1, 1, 2, 5, 15, 51,...) convolved with A006789 (1, 1, 2, 5, 14, 43,...) = A006789 shifted: (1, 2, 5, 14, 43, 143,...).
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LINKS
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FORMULA
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Convolution triangle by rows, T(n,k) = A153197(n-k) * A153198 = a * b, where a = an infinite lower triangular matrix with A153197 prefaced with a 1: (1, 1, 2, 5, 15, 51, 189, 748,...) in every column; and b = an infinite lower triangular matrix with A006789 in the main diagonal and the rest zeros.
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EXAMPLE
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First few rows of the triangle =
1;
1, 1;
2, 1, 2;
5, 2, 2, 5;
15, 5, 4, 5, 14;
51, 15, 10, 10, 14, 43;
189, 51, 30, 25, 28, 43, 143;
748, 189, 102, 75, 70, 86, 143, 509;
3128, 748, 378, 255, 210, 215, 286, 509, 1922;
13731, 3128, 1496, 945, 714, 645, 715, 1018, 1922, 7651;
62969, 13731, 6256, 3740, 2646, 2193, 2145, 2545, 3844, 7651, 31965;
...
Row 5 = (51, 15, 10, 10, 14, 43), = termwise products of (51, 15, 5, 2, 1, 1) and (1, 1, 2, 5, 14, 43), where A153197 = (1, 2, 5, 15, 51,...); and A006789 = (1, 1, 2, 5, 14, 43,...).
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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