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A104730
Triangle read by rows: T(n,k)=C(n+1,k)-C(k,n-k+1).
2
1, 1, 1, 1, 3, 1, 1, 4, 5, 1, 1, 5, 10, 7, 1, 1, 6, 15, 19, 9, 1, 1, 7, 21, 35, 31, 11, 1, 1, 8, 28, 56, 69, 46, 13, 1, 1, 9, 36, 84, 126, 121, 64, 15, 1, 1, 10, 45, 120, 210, 251, 195, 85, 17, 1, 1, 11, 55, 165, 330, 462, 456, 295, 109, 19, 1, 1, 12, 66
OFFSET
1,5
COMMENTS
Row sums are A027934: 1, 2, 5, 11, 24, 51, 107... Diagonal sums are A131298.
LINKS
FORMULA
Perform the operation A - B; then extract the triangle after deleting all zeros. P = infinite lower triangular Pascal's triangle matrix (A007318); B = A026729, as an infinite lower triangular matrix: [1; 0, 1;, 0, 1, 1; 0, 0, 2, 1; 0, 0, 1, 3, 1;...].
EXAMPLE
The first few rows of the triangle are:
1;
1, 1;
1, 3, 1;
1, 4, 5, 1;
1, 5, 10, 7, 1;
1, 6, 15, 19, 9, 1;
1, 7, 31, 35, 31, 11, 1;
...
MATHEMATICA
Table[Binomial[n+1, k]-Binomial[k, n-k+1], {n, 0, 20}, {k, 0, n}]//Flatten (* Harvey P. Dale, Jan 16 2024 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Mar 20 2005
EXTENSIONS
Better definition from Paul Barry, Jun 26 2007
More terms from Harvey P. Dale, Jan 16 2024
STATUS
approved