This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
print([sum(row) for row in A371994_triangle(17)])
Array starts: [0] 1, 1, 2, 5, 14, 42, 132, ... [1] 1, 1, 3, 15, 105, 945, 10395, ... [2] 1, 1, 5, 61, 1385, 50521, 2702765, ... [3] 1, 1, 9, 297, 24273, 3976209, 1145032281, ... [4] 1, 1, 17, 1585, 485729, 372281761, 601378506737, ... [5] 1, 1, 33, 8865, 10401345, 38103228225, 352780110115425, ... [6] 1, 1, 65, 50881, 231455105, 4104215813761, 220579355255364545, ... . Seen as a triangle T(n, k) = A(k, n - k): [0] [ 1] [1] [ 1, 1] [2] [ 2, 1, 1] [3] [ 5, 3, 1, 1] [4] [ 14, 15, 5, 1, 1] [5] [ 42, 105, 61, 9, 1, 1] [6] [132, 945, 1385, 297, 17, 1, 1] [7] [429, 10395, 50521, 24273, 1585, 33, 1, 1]
def GeneralizedDelehamDelta(F, dim, seq=True): # The algorithm.
ring = PolynomialRing(ZZ, 'x')
x = ring.gen()
A = [sum(F[j](k) * x^j for j in range(len(F))) for k in range(dim)]
C = [ring(0)] + [ring(1) for i in range(dim)]
for k in range(dim):
for n in range(k, 0, -1):
C[n] = C[n-1] + C[n+1] * A[n-1]
yield list(C[1])[-1] if seq else list(C[1])
def F(n): # Define the input functions.
def p0(): return lambda n: pow(n, n^0)
def p(k): return lambda n: pow(n + 1, k)
return [p0()] + [p(k) for k in range(n + 1)]
def A(n, dim): # Return only the main diagonal of the triangle.
return [r for r in GeneralizedDelehamDelta(F(n), dim)]
for n in range(7): print(A(n, 7))
def T(n, dim): # Return the regularized triangle.
R = GeneralizedDelehamDelta(F(n), dim, False)
return [[r[k] for k in range(0, len(r), n + 1)] for r in R]
for n in range(0, 4):
for row in T(n, 6): print(row)
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