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.
a[n_]:=(n^2-n)!; Array[a,9,0]
The irregular triangle begins:
1;
0;
0, 2;
0, 2;
0, 4;
0, 2, 6;
0, 2, 6;
0, 0, 12;
0, 0, 18;
0, 0, 24, 24;
0, 0, 30, 24;
0, 0, 42, 48;
0, 0, 42, 72;
0, 0, 48, 120;
0, 0, 48, 144, 120;
...
T(7,3) = 6 since we have: 1+2+4, 1+4+2, 2+1+4, 2+4+1, 4+1+2, 4+2+1.
Flatten[Table[Length[Select[Join@@Permutations/@Select[IntegerPartitions[n,All,Range[k^2]], UnsameQ@@#&], Length[#]==k&]], {n, 21}, {k, Floor[(Sqrt[8n+1]-1)/2]}]] (* After Gus Wiseman in A072574 *)
a(1) = A362209(1,1) = 1 since we have:
[1].
a(2) = A362209(5,2) = 8 since we have:
[1, 2] [1, 3] [4, 2] [4, 3]
[3, 4], [2, 4], [3, 1], [2, 1],
.
[2, 1] [2, 4] [3, 1] [3, 4]
[4, 3], [1, 3], [4, 2], [1, 2].
from math import factorial
from itertools import combinations as C
def a(n):
E = [i for i in range(1, n**2+1)]
m = n if n%2 == 0 else n-1
r = n**2 - 2*m
fm, fr = factorial(m), factorial(r)
p = fm**2 * fr
return p*sum(1 for u in C(E, 2*m) for t in C(u, m) if 2*sum(t)==sum(u))
print([a(n) for n in range(1, 5)])
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