login
a(n) is the permanent of the n X n matrix M(n) defined by M[i, j, n] = binomial(n*i, j).
0

%I #11 Oct 08 2023 10:27:05

%S 1,1,16,8343,191379456,243158252171875,20790955151695025307648,

%T 141077987559931565709345896142747,

%U 87560777683393072753972141033294994323013632,5630148253059996156951223684618938659855264355379747814715,41903151415731168301895742189359145224747037005872123307731920000000000000

%N a(n) is the permanent of the n X n matrix M(n) defined by M[i, j, n] = binomial(n*i, j).

%e a(3) = 8343:

%e [3, 3, 1]

%e [6, 15, 20]

%e [9, 36, 84]

%t a[n_]:=Permanent[Table[Binomial[n i,j],{i,n},{j,n}]]; Join[{1},Array[a,10]]

%o (PARI) a(n) = {matpermanent(matrix(n, n, i, j, binomial(n*i, j)))}; \\ _Vaclav Kotesovec_, Oct 08 2023

%Y Cf. A023813 (determinant).

%K nonn

%O 0,3

%A _Stefano Spezia_, Oct 08 2023