A108085 Triangle, read by rows, where T(0,0) = 1, T(n,k) = 2^n*T(n-1,k) - T(n-1,k-1).

1, 2, -1, 8, -6, 1, 64, -56, 14, -1, 1024, -960, 280, -30, 1, 32768, -31744, 9920, -1240, 62, -1, 2097152, -2064384, 666624, -89280, 5208, -126, 1, 268435456, -266338304, 87392256, -12094464, 755904, -21336, 254, -1, 68719476736, -68451041280, 22638755840, -3183575040, 205605888, -6217920

Offset: 0

Author

Gerald McGarvey, Jun 05 2005

Keywords

• sign
• tabl

Comments

For n > 0, n-th row sum = Product_{i=1..n} (2^i - 1), i.e., A005329(n).

Triangle T(n,k), 0 <= k <= n, read by rows given by [2, 2, 8, 12, 32, 56, 128, 240, 512, ...] DELTA [-1, 0, -2, 0, -4, 0, -8, 0, -16, 0, -32, 0, ...] = A014236(first zero omitted)DELTA -A077957 where DELTA is the operator defined in A084938. - Philippe Deléham, Aug 23 2006

Examples

			Triangle begins
     1;
     2,   -1;
     8,   -6,   1;
    64,  -56,  14,  -1;
  1024, -960, 280, -30, 1;
		

Programs

PARI

t(n, k) = {if (k < 0, return (0)); if (n < k, return (0)); if (n == 0, return (1)); return (2^n*t(n-1,k) - t(n-1,k-1));}  \\ Michel Marcus, Apr 11 2013