# SageMath code for A330794 in one unit. # code based on Peter Luschny's work max = 20 # number of rows of the matrix def riordan_array(d, h, n, exp=false): def taylor_list(f, n): t = SR(f).taylor(x, 0, n-1).list() return t + [0]*(n-len(t)) td = taylor_list(d, n) th = taylor_list(h, n) M = matrix(QQ, n, n) for k in (0..n-1): M[k, 0] = td[k] for k in (1..n-1): for m in (k..n-1): M[m, k] = add(M[j, k-1]*th[m-j] for j in (k-1..m-1)) if exp: u = 1 for k in (1..n-1): u *= k for m in (0..k): j = u if m==0 else j/m M[k, m] *= j return M riordan_array(1, 1/(2-exp(x)) - 1, 8, exp=true) def riordan_square(gf, len, exp=false): return riordan_array(gf, gf, len, exp) # A322942 = riordan_square((1 - 2*x^2)/((1 + x)*(1 - 2*x)), max+2) A330794 = riordan_square((1 - 2*x^2)/((1 + x)*(1 - 2*x)), max+2).inverse() # inverse of A322942 # [[A330794[n,k] for k in range(n+1)] for n in range(max+1)] # triangle form of A330794 flatten([[A330794[n,k] for k in range(n+1)] for n in range(max+1)]) # flattened triangle