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A140136
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Numerator coefficients for generators of lattice path enumeration square array A111910.
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0
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1, 1, 1, 1, 7, 7, 1, 1, 20, 75, 75, 20, 1, 1, 42, 364, 1001, 1001, 364, 42, 1, 1, 75, 1212, 6720, 15288, 15288, 6720, 1212, 75, 1, 1, 121, 3223, 30723, 127908, 255816, 255816, 127908, 30723, 3223, 121, 1, 1, 182, 7371, 109538, 737737, 2510508
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| sum{k=0..n, T(n,k)x^k}/(1-x)^(3n+1) generates row n of A111910.
Row sums are A006335. - Paul Barry (pbarry(AT)wit.ie), May 09 2008
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REFERENCES
| G. Kreweras and H. Niederhausen, Solution of an enumerative problem connected with lattice paths, European J. Combin., 2 (1981), 55-60.
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FORMULA
| Triangle T(q,n) where T(n,q)=sum{j=0..n, (-1)^j*C(3q+1,j)*K(n-j,q)} with K(p,q)=A111910(p,q).
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EXAMPLE
| Triangle begins
1,
1,1,
1,7,7,1,
1,20,75,75,20,1,
1,42,364,1001,1001,364,42,1,
1,75,1212,6720,15288,15288,6720,1212,75,1
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CROSSREFS
| Sequence in context: A200622 A046542 A172351 * A171707 A156722 A152565
Adjacent sequences: A140133 A140134 A140135 * A140137 A140138 A140139
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 09 2008
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