A132823 - OEIS

A132823

Triangle read by rows: T(n,k) = binomial(n,k) - 2 for 0 < k < n, with T(n,0) = T(n,n) = 1.

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 4, 2, 1, 1, 3, 8, 8, 3, 1, 1, 4, 13, 18, 13, 4, 1, 1, 5, 19, 33, 33, 19, 5, 1, 1, 6, 26, 54, 68, 54, 26, 6, 1, 1, 7, 34, 82, 124, 124, 82, 34, 7, 1, 1, 8, 43, 118, 208, 250, 208, 118, 43, 8, 1, 1, 9, 53, 163, 328, 460, 460, 328, 163, 53, 9, 1

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OFFSET

0,12

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)

FORMULA

Equals A007318 + 2*A103451 - 2*A000012 as infinite lower triangular matrices.

T(2*n,n) = A115112(n) for n > 0.

G.f.: 1/(1 - x - x*y) - 2*y*x^2/((1 - x)*(1 - y*x)). - Andrew Howroyd, Nov 17 2025

EXAMPLE

First few rows of the triangle:

1, 1;