A375025 Triangle read by rows: Matrix inverse of row-reversed A374439.
1, -2, 1, 3, -2, 1, -4, 2, -2, 1, 6, -2, 1, -2, 1, -10, 5, 0, 0, -2, 1, 15, -10, 5, 2, -1, -2, 1, -20, 10, -12, 6, 4, -2, -2, 1, 30, -8, 4, -16, 8, 6, -3, -2, 1, -52, 26, 8, -4, -22, 11, 8, -4, -2, 1, 78, -60, 30, 30, -15, -30, 15, 10, -5, -2, 1
Offset: 0
Examples
Triangle starts: [0] [ 1] [1] [ -2, 1] [2] [ 3, -2, 1] [3] [ -4, 2, -2, 1] [4] [ 6, -2, 1, -2, 1] [5] [-10, 5, 0, 0, -2, 1] [6] [ 15, -10, 5, 2, -1, -2, 1] [7] [-20, 10, -12, 6, 4, -2, -2, 1] [8] [ 30, -8, 4, -16, 8, 6, -3, -2, 1] [9] [-52, 26, 8, -4, -22, 11, 8, -4, -2, 1]
Programs
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Maple
A := (n,k) -> ifelse(k::odd,2,1)*binomial(n-irem(k,2)-iquo(k,2),iquo(k,2)): ARevRow := n -> local k; [seq(A(n, n-k), k = 0..n)]: M := m -> Matrix(m, (n, k) -> ifelse(k > n, 0, ARevRow(n-1)[k])): T := n -> LinearAlgebra:-MatrixInverse(M(n)): T(11);
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Python
from functools import cache @cache def Trow(n): if n == 0: return [1] if n == 1: return [-2, 1] fli = Trow(n - 1) row = [1] * (n + 1) row[n - 1] = -2 for k in range(n - 2, 0, -1): row[k] = fli[k - 1] - fli[k + 1] row[0] = -2 * fli[0] - fli[1] return row # Peter Luschny, Aug 18 2024