A370890 A(n, k) = 2^n*Pochhammer(k/2, floor((n+1)/2)). Square array read by ascending antidiagonals.
1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 6, 4, 3, 1, 0, 12, 16, 6, 4, 1, 0, 60, 32, 30, 8, 5, 1, 0, 120, 192, 60, 48, 10, 6, 1, 0, 840, 384, 420, 96, 70, 12, 7, 1, 0, 1680, 3072, 840, 768, 140, 96, 14, 8, 1, 0, 15120, 6144, 7560, 1536, 1260, 192, 126, 16, 9, 1
Offset: 0
Examples
The array starts: [0] 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... [1] 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ... [2] 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, ... [3] 0, 6, 16, 30, 48, 70, 96, 126, 160, 198, ... [4] 0, 12, 32, 60, 96, 140, 192, 252, 320, 396, ... [5] 0, 60, 192, 420, 768, 1260, 1920, 2772, 3840, 5148, ... . Seen as the triangle T(n, k) = A(n - k, k): [0] 1; [1] 0, 1; [2] 0, 1, 1; [3] 0, 2, 2, 1; [4] 0, 6, 4, 3, 1; [5] 0, 12, 16, 6, 4, 1; [6] 0, 60, 32, 30, 8, 5, 1; [7] 0, 120, 192, 60, 48, 10, 6, 1;
Links
- Paolo Xausa, Table of n, a(n) for n = 0..11324 (first 150 antidiagonals, flattened).
Crossrefs
Programs
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Maple
A := (n, k) -> 2^n*pochhammer(k/2, iquo(n+1,2)): for n from 0 to 5 do seq(A(n, k), k = 0..9) od; T := (n, k) -> A(n - k, k): seq(seq(T(n, k), k = 0..n), n = 0..10);
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Mathematica
A370890[n_, k_] := 2^n*Pochhammer[k/2, Floor[(n+1)/2]]; Table[A370890[n-k, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Mar 06 2024 *)
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SageMath
# Note the use of different kinds of division. def A(n, k): return 2**n * rising_factorial(k/2, (n+1)//2) for n in range(0, 9): print([A(n, k) for k in range(0, 9)])