A126127 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

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:

-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

Cf. A061554, A046854.

Sequence in context: A337366 A153917 A326407 * A230324 A060256 A103899

Adjacent sequences: A126124 A126125 A126126 * A126128 A126129 A126130

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Dec 17 2006

STATUS

approved