OFFSET
1,4
FORMULA
T(n, k) = (2^n - 2^(n-k-1) - 2^k)*binomial(n-1, k), for n >= 1 and 0 <= k <= n-1.
EXAMPLE
Triangle begins:
0;
1, 1;
3, 8, 3;
7, 30, 30, 7;
15, 88, 144, 88, 15;
31, 230, 520, 520, 230, 31;
63, 564, 1620, 2240, 1620, 564, 63;
127, 1330, 4620, 8120, 8120, 4620, 1330, 127;
255, 3056, 12432, 26432, 33600, 26432, 12432, 3056, 255;
511, 6894, 32112, 79968, 122976, 122976, 79968, 32112, 6894, 511;
1023, 15340, 80460, 229440, 413280, 499968, 413280, 229440, 80460, 15340, 1023;
...
MAPLE
T := n -> local k; seq((2^n - 2^(n - k - 1) - 2^k)*binomial(n - 1, k), k = 0 .. n - 1);
seq(T(n), n = 1 .. 11);
MATHEMATICA
T[n_, k_] := (2^n - 2^(n - k - 1) - 2^k)*Binomial[n - 1, k]; Table[T[n, k], {n, 1, 10}, {k, 0, n - 1}] // Flatten (* Amiram Eldar, Dec 20 2022 *)
CROSSREFS
KEYWORD
AUTHOR
Ambrosio Valencia-Romero, Dec 20 2022
STATUS
approved