A126127 Inverse square of A061554.

1, -2, 1, -1, -2, 1, 5, -3, -2, 1, 2, 9, -5, -2, 1, -13, 9, 13, -7, -2, 1, -5, -33, 20, 17, -9, -2, 1, 34, -27, -61, 35, 21, -11, -2, 1, 13, 111, -73, -97, 54, 25, -13, -2, 1, -89, 80, 248, -151, -141, 77, 29, -15, -2, 1, -34, -355, 252, 461, -269, -193, 104, 33, -17, -2, 1

Offset: 0

Author

Gary W. Adamson, Dec 17 2006

Keywords

• tabl
• sign

Comments

Inverse of A061554 = A046854; therefore A126127 = (A046854)^2.

Examples

			First few rows of the triangle are:
1;
-2, 1;
-1, -2, 1;
5, -3, -2, 1;
2, 9, -5, -2, 1;
-13, 9, 13, -7, -2, 1;
...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10009 (rows 0 to 140, flattened)

Crossrefs

Cf. A061554, A046854.

Programs

Maple

T:= Matrix(20,20,(n,k) -> binomial(n-1, floor((n)/2 - (-1)^(n-k)*(k)/2)), shape=triangular[lower]):
A:= T^(-2):
seq(seq(A[i,k],k=1..i),i=1..20); # Robert Israel, Jul 07 2019

Formula

Given M = Pascal's triangle with descending row terms, (A061554); A126127 = M^(-2).

G.f. as triangle (conjectured): (1-x)*(1-x+x^2)/(1-x*y+3*x^2-x^3*y+x^4). - Robert Israel, Jul 07 2019