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A165408
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An aerated Catalan array.
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3
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1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 2, 0, 4, 0, 1, 0, 0, 0, 5, 0, 5, 0, 1, 0, 0, 0, 0, 9, 0, 6, 0, 1, 0, 0, 0, 5, 0, 14, 0, 7, 0, 1, 0, 0, 0, 0, 14, 0, 20, 0, 8, 0, 1, 0, 0, 0, 0, 0, 28, 0, 27, 0, 9, 0, 1, 0, 0, 0, 0, 14, 0, 48, 0, 35, 0, 10, 0, 1, 0, 0, 0, 0, 0, 42, 0, 75, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| Aeration of A120730. Row sums are A165407.
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FORMULA
| Number triangle T(n,k)=if(n<=3k, C((n+k)/2,k)*((3k-n)/2+1)*(1+(-1)^(n-k))/(2(k+1)),0);
G.f.: 1/(1-xy-x^3y/(1-x^3y/(1-x^3y/(1-x^3y/(1-... (continued fraction).
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EXAMPLE
| Triangle begins
1,
0, 1,
0, 0, 1,
0, 1, 0, 1,
0, 0, 2, 0, 1,
0, 0, 0, 3, 0, 1,
0, 0, 2, 0, 4, 0, 1,
0, 0, 0, 5, 0, 5, 0, 1,
0, 0, 0, 0, 9, 0, 6, 0, 1,
0, 0, 0, 5, 0, 14, 0, 7, 0, 1,
0, 0, 0, 0, 14, 0, 20, 0, 8, 0, 1,
0, 0, 0, 0, 0, 28, 0, 27, 0, 9, 0, 1,
0, 0, 0, 0, 14, 0, 48, 0, 35, 0, 10, 0, 1
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CROSSREFS
| Sequence in context: A187144 A123635 A124304 * A171368 A089812 A133988
Adjacent sequences: A165405 A165406 A165407 * A165409 A165410 A165411
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 17 2009
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