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

0,8

Links

Paolo Xausa, Table of n, a(n) for n = 0..11324 (first 150 antidiagonals, flattened).

Example

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;

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);

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 *)

Prog

(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)])

Crossrefs

Rows: A000012, A001477, A005843, A054000, A134582.

Columns: A000007, A081125, A355989.

Cf. A370419.

Sequence in context: A064045 A258829 A110314 * A152882 A130167 A084938

Adjacent sequences: A370887 A370888 A370889 * A370891 A370892 A370893

Keyword

nonn,tabl

Author

Peter Luschny, Mar 04 2024

Status

approved