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A203433 Vandermonde determinant of the first n terms of (2,3,5,6,8,9,...) = (j+floor((j+1)/2)).

%I A203433 #12 Sep 20 2023 01:45:30
%S A203433 1,1,6,72,12960,6531840,84652646400,3839844040704000,
%T A203433 6568897997313146880000,46482573252667397426380800000,
%U A203433 16698920220108665726304214056960000000,28359415513133792655802758561911537664000000000
%N A203433 Vandermonde determinant of the first n terms of (2,3,5,6,8,9,...) = (j+floor((j+1)/2)).
%C A203433 Each term divides its successor, as in A014402, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203434.
%H A203433 G. C. Greubel, <a href="/A203433/b203433.txt">Table of n, a(n) for n = 1..41</a>
%t A203433 f[j_]:= j + Floor[(j+1)/2]; z = 20;
%t A203433 v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
%t A203433 d[n_]:= Product[(i-1)!, {i,n}]
%t A203433 Table[v[n], {n,z}]             (* this sequence *)
%t A203433 Table[v[n+1]/v[n], {n,z}]      (* A014402 *)
%t A203433 Table[v[n]/d[n], {n,z}]        (* A203434 *)
%o A203433 (Magma)
%o A203433 A203433:= func< n | n eq 1 select 1 else (&*[(&*[k-j+Floor(k/2)-Floor(j/2): j in [0..k-1]]) : k in [1..n-1]]) >;
%o A203433 [A203433(n): n in [1..25]]; // _G. C. Greubel_, Sep 20 2023
%o A203433 (SageMath)
%o A203433 def A203433(n): return product(product(k-j+(k//2)-(j//2) for j in range(k)) for k in range(1,n))
%o A203433 [A203433(n) for n in range(1,31)] # _G. C. Greubel_, Sep 20 2023
%Y A203433 Cf. A000178, A007494, A014402, A203434.
%K A203433 nonn
%O A203433 1,3
%A A203433 _Clark Kimberling_, Jan 02 2012