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A126127
Inverse square of A061554.
1
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
0,2
COMMENTS
Inverse of A061554 = A046854; therefore A126127 = (A046854)^2.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10009 (rows 0 to 140, flattened)
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
EXAMPLE
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;
...
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
CROSSREFS
Sequence in context: A337366 A153917 A326407 * A230324 A060256 A103899
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Dec 17 2006
STATUS
approved