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1, 0, 1, 1, 0, 2, 0, 2, 0, 3, 2, 0, 6, 0, 6, 0, 5, 0, 12, 0, 10, 5, 0, 18, 0, 30, 0, 20, 0, 14, 0, 42, 0, 60, 0, 35, 14, 0, 56, 0, 120, 0, 140, 0, 70, 0, 42, 0, 144, 0, 270, 0, 280, 0, 126
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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COMMENTS
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Row sums = A145974: (1, 1, 3, 5, 14, 27, 73,...).
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LINKS
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Table of n, a(n) for n=0..54.
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FORMULA
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Convolution triangle, A053121 * (A001405 * 0^(n-k)).
A053121 = the aerated Catalan triangle and (A001405 * 0^(n-k) = an
infinite lower triangular matrix with A001405 as the main diagonal and
the rest zeros.
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EXAMPLE
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First few rows of the triangle =
1;
0, 1;
1, 0, 2;
0, 2, 0, 3;
2, 0, 6, 0, 6;
0, 5, 0, 12, 0, 10;
5, 0, 18, 0, 30, 0, 20;
0, 14, 0, 42, 0, 60, 0, 35;
14, 0, 56, 0, 120, 0, 140, 0, 70;
0, 42, 0, 144, 0, 270, 0, 280, 0, 126;
42, 0, 180, 0, 450, 0, 700, 0, 630, 0, 252;
...
Example: Row 4 = (2, 0, 6, 0, 6) = termwise products of (2, 0, 3, 0, 1) and (1, 1, 2, 3, 6).
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CROSSREFS
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Sequence in context: A029224 A029188 A090290 * A169611 A144494 A136166
Adjacent sequences: A153582 A153583 A153584 * A153586 A153587 A153588
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Dec 28 2008
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STATUS
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approved
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