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A307668
A(n,k) = Sum_{j=0..floor(n/k)} (-1)^j*binomial(2*n,k*j+n), square array A(n,k) read by antidiagonals, for n >= 0, k >= 1.
1
1, 1, 1, 1, 2, 3, 1, 2, 5, 10, 1, 2, 6, 14, 35, 1, 2, 6, 19, 43, 126, 1, 2, 6, 20, 62, 142, 462, 1, 2, 6, 20, 69, 207, 494, 1716, 1, 2, 6, 20, 70, 242, 705, 1780, 6435, 1, 2, 6, 20, 70, 251, 858, 2445, 6563, 24310, 1, 2, 6, 20, 70, 252, 912, 3068, 8622, 24566, 92378
OFFSET
0,5
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 2, 2, 2, 2, 2, 2, ...
3, 5, 6, 6, 6, 6, 6, ...
10, 14, 19, 20, 20, 20, 20, ...
35, 43, 62, 69, 70, 70, 70, ...
126, 142, 207, 242, 251, 252, 252, ...
462, 494, 705, 858, 912, 923, 924, ...
1716, 1780, 2445, 3068, 3341, 3418, 3431, ...
6435, 6563, 8622, 11051, 12310, 12750, 12854, ...
MATHEMATICA
T[n_, k_] := Sum[(-1)^j*Binomial[2*n, k*j + n], {j, 0, Floor[n/k]}]; Table[T[n - k, k], {n, 0, 11}, {k, n, 1, -1}] // Flatten (* Amiram Eldar, May 13 2021*)
CROSSREFS
Columns 1-2 give A088218, A005317.
Sequence in context: A362599 A245559 A117488 * A308173 A256910 A181176
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Apr 20 2019
STATUS
approved