A360859 Triangle read by rows. T(n, k) = binomial(n, ceil(k/2)) * binomial(n, floor(k/2)).
1, 1, 1, 1, 2, 4, 1, 3, 9, 9, 1, 4, 16, 24, 36, 1, 5, 25, 50, 100, 100, 1, 6, 36, 90, 225, 300, 400, 1, 7, 49, 147, 441, 735, 1225, 1225, 1, 8, 64, 224, 784, 1568, 3136, 3920, 4900, 1, 9, 81, 324, 1296, 3024, 7056, 10584, 15876, 15876, 1, 10, 100, 450, 2025, 5400, 14400, 25200, 44100, 52920, 63504
Offset: 0
Examples
Triangle T(n, k) starts: [0] 1; [1] 1, 1; [2] 1, 2, 4; [3] 1, 3, 9, 9; [4] 1, 4, 16, 24, 36; [5] 1, 5, 25, 50, 100, 100; [6] 1, 6, 36, 90, 225, 300, 400; [7] 1, 7, 49, 147, 441, 735, 1225, 1225; [8] 1, 8, 64, 224, 784, 1568, 3136, 3920, 4900; [9] 1, 9, 81, 324, 1296, 3024, 7056, 10584, 15876, 15876;
Programs
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Maple
A360859 := (n, k) -> binomial(n, ceil(k/2)) * binomial(n, floor(k/2)): seq(seq(A360859(n, k), k = 0..n), n = 0..10);
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Python
from math import comb def A360859_T(n,k): return comb(n,m:=k>>1)**2*(n-m)//(m+1) if k&1 else comb(n,k>>1)**2 # Chai Wah Wu, Feb 28 2023