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A293960
Number A(n,k) of linear chord diagrams having n chords and no chord length larger than k; square array A(n,k), n>=0, k>=0, read by antidiagonals.
10
1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 3, 1, 0, 1, 1, 3, 5, 1, 0, 1, 1, 3, 15, 11, 1, 0, 1, 1, 3, 15, 35, 21, 1, 0, 1, 1, 3, 15, 105, 103, 43, 1, 0, 1, 1, 3, 15, 105, 315, 343, 85, 1, 0, 1, 1, 3, 15, 105, 945, 1141, 979, 171, 1, 0, 1, 1, 3, 15, 105, 945, 3465, 4779, 2915, 341, 1, 0
OFFSET
0,13
COMMENTS
All terms in columns k > 0 are odd.
LINKS
FORMULA
A(n,k) = Sum_{j=0..k} A293961(n,j).
A(n,k) = A(n,n) = A001147(n) for k >= n.
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 3, 3, 3, 3, 3, 3, ...
0, 1, 5, 15, 15, 15, 15, 15, ...
0, 1, 11, 35, 105, 105, 105, 105, ...
0, 1, 21, 103, 315, 945, 945, 945, ...
0, 1, 43, 343, 1141, 3465, 10395, 10395, ...
0, 1, 85, 979, 4779, 14857, 45045, 135135, ...
CROSSREFS
Main diagonal gives A001147.
Cf. A293961.
Sequence in context: A355692 A192003 A226873 * A062719 A305161 A250484
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Oct 20 2017
STATUS
approved