OFFSET
0,3
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).
FORMULA
A357367(n, k) = n!*T(n, k).
EXAMPLE
Triangle begins:
[0] 1;
[1] 0, 2;
[2] 0, 3, 6;
[3] 0, 4, 20, 20;
[4] 0, 5, 45, 105, 70;
[5] 0, 6, 84, 336, 504, 252;
[6] 0, 7, 140, 840, 2100, 2310, 924;
[7] 0, 8, 216, 1800, 6600, 11880, 10296, 3432;
.
Seen as an array A(n, k) = binomial(n + k - 1, n)*binomial(n + 2*k, k):
[0] 1, 2, 6, 20, 70, 252, 924, ... [A000984]
[1] 0, 3, 20, 105, 504, 2310, 10296, ... [A000917]
[2] 0, 4, 45, 336, 2100, 11880, 63063, ...
[3] 0, 5, 84, 840, 6600, 45045, 280280, ...
[4] 0, 6, 140, 1800, 17325, 140140, 1009008, ...
[5] 0, 7, 216, 3465, 40040, 378378, 3118752, ...
[6] 0, 8, 315, 6160, 84084, 917280, 8576568, ...
MAPLE
T := (n, k) -> binomial(n - 1, k - 1)*binomial(n + k, k): seq(seq(T(n, k), k = 0..n), n = 0..9);
MATHEMATICA
A386789[n_, k_] := Binomial[n - 1, k - 1]*Binomial[n + k, k];
Table[A386789[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Aug 06 2025 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Aug 06 2025
STATUS
approved
