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URL: https://oeis.org/A306680

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A306680
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-1))/((1-x)^k-x^(k+1)).
9
1, 1, 2, 1, 1, 3, 1, 1, 2, 4, 1, 1, 1, 3, 5, 1, 1, 1, 2, 5, 6, 1, 1, 1, 1, 4, 8, 7, 1, 1, 1, 1, 2, 7, 13, 8, 1, 1, 1, 1, 1, 5, 12, 21, 9, 1, 1, 1, 1, 1, 2, 11, 21, 34, 10, 1, 1, 1, 1, 1, 1, 6, 21, 37, 55, 11, 1, 1, 1, 1, 1, 1, 2, 16, 37, 65, 89, 12
OFFSET
0,3
LINKS
FORMULA
A(n,k) = Sum_{j=0..n} binomial(n-j,k*j).
A(n,k) = A306713(k*n,k) for k > 0.
EXAMPLE
A(4,1) = A306713(4,1) = 5, A(4,2) = A306713(8,2) = 4.
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2, 1, 1, 1, 1, 1, 1, 1, 1, ...
3, 2, 1, 1, 1, 1, 1, 1, 1, ...
4, 3, 2, 1, 1, 1, 1, 1, 1, ...
5, 5, 4, 2, 1, 1, 1, 1, 1, ...
6, 8, 7, 5, 2, 1, 1, 1, 1, ...
7, 13, 12, 11, 6, 2, 1, 1, 1, ...
8, 21, 21, 21, 16, 7, 2, 1, 1, ...
9, 34, 37, 37, 36, 22, 8, 2, 1, ...
MATHEMATICA
T[n_, k_] := Sum[Binomial[n - j, k*j], {j, 0, n}]; Table[T[k, n - k], {n, 0, 11}, {k, 0, n}] // Flatten (* Amiram Eldar, Jun 21 2021 *)
CROSSREFS
Columns 0-9 give A000027(n+1), A000045(n+1), A005251(n+1), A003522, A005676, A099132, A293169, A306721, A306752, A306753.
Sequence in context: A205131 A175892 A010783 * A083312 A032435 A337798
KEYWORD
nonn,tabl,look
AUTHOR
Seiichi Manyama, Mar 05 2019
STATUS
approved