A060539 Table by antidiagonals of number of ways of choosing k items from n*k.
1, 1, 2, 1, 6, 3, 1, 20, 15, 4, 1, 70, 84, 28, 5, 1, 252, 495, 220, 45, 6, 1, 924, 3003, 1820, 455, 66, 7, 1, 3432, 18564, 15504, 4845, 816, 91, 8, 1, 12870, 116280, 134596, 53130, 10626, 1330, 120, 9, 1, 48620, 735471, 1184040, 593775, 142506, 20475, 2024, 153, 10
Offset: 1
Examples
Square array A(n,k) begins: 1, 1, 1, 1, 1, 1, 1, ... 2, 6, 20, 70, 252, 924, 3432, ... 3, 15, 84, 495, 3003, 18564, 116280, ... 4, 28, 220, 1820, 15504, 134596, 1184040, ... 5, 45, 455, 4845, 53130, 593775, 6724520, ... 6, 66, 816, 10626, 142506, 1947792, 26978328, ... 7, 91, 1330, 20475, 324632, 5245786, 85900584, ...
Links
- Seiichi Manyama, Antidiagonals n = 1..140, flattened (first 20 antidiagonals from Harry J. Smith)
- H. J. Brothers, Pascal's Prism: Supplementary Material.
Crossrefs
Programs
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Maple
A:= (n, k)-> binomial(n*k, k): seq(seq(A(n, 1+d-n), n=1..d), d=1..10); # Alois P. Heinz, Jul 28 2023
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PARI
{ i=0; for (m=1, 20, for (n=1, m, k=m - n + 1; write("b060539.txt", i++, " ", binomial(n*k, k))); ) } \\ Harry J. Smith, Jul 06 2009