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A358146
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} binomial(k*j,j).
2
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 9, 4, 1, 1, 5, 19, 29, 5, 1, 1, 6, 33, 103, 99, 6, 1, 1, 7, 51, 253, 598, 351, 7, 1, 1, 8, 73, 506, 2073, 3601, 1275, 8, 1, 1, 9, 99, 889, 5351, 17577, 22165, 4707, 9, 1, 1, 10, 129, 1429, 11515, 58481, 152173, 138445, 17577, 10, 1
OFFSET
0,5
LINKS
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, ...
1, 3, 9, 19, 33, 51, ...
1, 4, 29, 103, 253, 506, ...
1, 5, 99, 598, 2073, 5351, ...
1, 6, 351, 3601, 17577, 58481, ...
PROG
(PARI) T(n, k) = sum(j=0, n, binomial(k*j, j));
CROSSREFS
Columns k=0-5 give: A000012, A001477(n+1), A006134, A188675, A225612, A225615.
Main diagonal gives A226391.
Cf. A358050.
Sequence in context: A295205 A297020 A099597 * A283113 A123610 A209631
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 31 2022
STATUS
approved