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.
[0] 1; [1] 1, 1; [2] 3, 6, 3; [3] 13, 39, 39, 13; [4] 75, 300, 450, 300, 75; [5] 541, 2705, 5410, 5410, 2705, 541; [6] 4683, 28098, 70245, 93660, 70245, 28098, 4683;
def TransOrdPart(m, n) -> list[int]:
@cached_function
def P(m: int, n: int):
R = PolynomialRing(ZZ, "x")
if n == 0: return R(1)
return R(sum(binomial(m * n, m * k) * P(m, n - k) * x
for k in range(1, n + 1)))
T = P(m, n)
def C(k) -> int:
return sum(T[j] * binomial(n, k) for j in range(n + 1))
return [C(k) for k in range(n+1)]
def A362585(n) -> list[int]: return TransOrdPart(1, n)
for n in range(6): print(A362585(n))
[0] 1; [1] 1, 1; [2] 21, 42, 21; [3] 1849, 5547, 5547, 1849; [4] 426405, 1705620, 2558430, 1705620, 426405; [5] 203374081, 1016870405, 2033740810, 2033740810, 1016870405, 203374081;