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.
%I A381723 #17 Mar 26 2025 08:28:14 %S A381723 1,4,225,27728,7240350,3439197360,2686774125000,3213645578293248, %T A381723 5578750547986764960,13484491722080225280000, %U A381723 43904082301794970311672000,187409206411313292409598115840,1025421491750171253824589270768000,7056011383804251291488039375527526400 %N A381723 a(n) = pos(M(n)), where M(n) is the n X n matrix with numbers 1, 2, ..., n^2 in order across rows, and pos(M(n)) is the positive part of the determinant of M(n); see A380661. %F A381723 a(n) = A232773(n)/2 for n >= 3. %e A381723 M(3) is the matrix with rows (1,2,3), (4,5,6), (7,8,9), determinant 0, permanent 450, negative part -225, and positive part 225. %t A381723 r[m_, n_] := Range[(m - 1) n + 1, m n]; %t A381723 d = Table[Det[Table[r[m, n], {m, 1, n}]], {n, 1, 15}] %t A381723 p = Table[Permanent[Table[r[m, n], {m, 1, n}]], {n, 1, 15}] %t A381723 neg = (d - p)/2 %t A381723 pos = (d + p)/2 %o A381723 (Python) %o A381723 from sympy.functions.combinatorial.numbers import stirling, factorial %o A381723 def A381723(n): return abs(sum(n**k*stirling(n,n-k,kind=1,signed=True)*stirling(n+1,k+1,kind=1,signed=True)*factorial(n-k)*factorial(k) for k in range(n+1)))>>1 if n>2 else 3*n-2 # _Chai Wah Wu_, Mar 25 2025 %Y A381723 Cf. A232773, A380661, A380662. %K A381723 nonn %O A381723 1,2 %A A381723 _Clark Kimberling_, Mar 09 2025