A136502 Matrix inverse of triangle A136501, read by rows.

1, -1, 1, 2, -2, 1, -7, 7, -4, 1, 44, -44, 26, -8, 1, -516, 516, -308, 100, -16, 1, 11622, -11622, 6959, -2296, 392, -32, 1, -512022, 512022, -306888, 101754, -17712, 1552, -64, 1, 44588536, -44588536, 26732904, -8877272, 1554404, -139104, 6176, -128, 1

Offset: 0

Author

Paul D. Hanna, Jan 01 2008

Keywords

• sign
• tabl

Examples

			Triangle begins:
1;
-1, 1;
2, -2, 1;
-7, 7, -4, 1;
44, -44, 26, -8, 1;
-516, 516, -308, 100, -16, 1;
11622, -11622, 6959, -2296, 392, -32, 1;
-512022, 512022, -306888, 101754, -17712, 1552, -64, 1;
44588536, -44588536, 26732904, -8877272, 1554404, -139104, 6176, -128, 1;
		

Crossrefs

Cf. A107354 (column 0), A136503 (column 2), A136504 (row sums) ; A136501 (matrix inverse).

Programs

PARI

{T(n,k)=local(M=matrix(n+1,n+1,r,c,binomial(2^(c-1),r-c)));(M^-1)[n+1,k+1]}

Formula

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