|
Search: id:A140136
|
|
|
| A140136 |
|
Numerator coefficients for generators of lattice path enumeration square array A111910. |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
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
|
|
REFERENCES
|
G. Kreweras and H. Niederhausen, Solution of an enumerative problem connected with lattice paths, European J. Combin., 2 (1981), 55-60.
|
|
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).
|
|
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
|
|
CROSSREFS
|
Sequence in context: A019725 A064890 A046542 this_sequence A156722 A152565 A146322
Adjacent sequences: A140133 A140134 A140135 this_sequence A140137 A140138 A140139
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), May 09 2008
|
|
|
Search completed in 0.002 seconds
|
