A137156 Matrix inverse of triangle A137153(n,k) = C(2^k+n-k-1, n-k), read by rows.

1, -1, 1, 1, -2, 1, -2, 5, -4, 1, 9, -24, 22, -8, 1, -88, 239, -228, 92, -16, 1, 1802, -4920, 4749, -1976, 376, -32, 1, -75598, 206727, -200240, 84086, -16432, 1520, -64, 1, 6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1

Offset: 0

Author

Paul D. Hanna, Jan 24 2008

Keywords

• sign
• tabl

Comments

Unsigned column 0 = A001192, number of full sets of size n.

Examples

			Triangle begins:
        1;
       -1,         1;
        1,        -2,        1;
       -2,         5,       -4,        1;
        9,       -24,       22,       -8,       1;
      -88,       239,     -228,       92,     -16,       1;
     1802,     -4920,     4749,    -1976,     376,     -32,    1;
   -75598,    206727,  -200240,    84086,  -16432,    1520,  -64,    1;
  6421599, -17568408, 17034964, -7173240, 1413084, -133984, 6112, -128, 1;
  ...
		

Crossrefs

Cf. A137153 (matrix inverse); unsigned columns: A001192, A137157, A137158, A137159; unsigned row sums: A137160.

Programs

PARI

/* As matrix inverse of A137153: */
{T(n,k) = local(M=matrix(n+1,n+1,r,c,if(r>=c,binomial(2^(c-1)+r-c-1,r-c)))); if(n
				

PARI

/* Using the g.f.: */
{T(n,k) = if(n
				

Formula

G.f. of column k: 1 = Sum_{n>=0} T(n+k,k)*x^n/(1-x)^(2^(n+k)).