A359200 Triangle read by rows: T(n, k) = A358125(n,k)*binomial(n-1, k), 0 <= k <= n-1.

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

Offset: 1

Author

Ambrosio Valencia-Romero, Dec 20 2022

Keywords

• nonn
• easy
• tabl

Examples

			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;
...
		

Crossrefs

Row sums give 2*A005061(n-1).

Programs

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 *)

Formula

T(n, k) = (2^n - 2^(n-k-1) - 2^k)*binomial(n-1, k), for n >= 1 and 0 <= k <= n-1.