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A203430 Vandermonde determinant of the first n numbers (1,3,4,6,7,9,10,...) = (j+floor(j/2)).

%I A203430 #12 Sep 28 2023 02:03:55
%S A203430 1,2,6,180,12960,18662400,84652646400,12068081270784000,
%T A203430 6568897997313146880000,157325632547489652827750400000,
%U A203430 16698920220108665726304214056960000000,101984821172231138973752227905335721984000000000
%N A203430 Vandermonde determinant of the first n numbers (1,3,4,6,7,9,10,...) = (j+floor(j/2)).
%C A203430 Each term divides its successor, as in A203431, and each term is divisible by the corresponding superfactorial, A000178(n), as in A203432.
%H A203430 G. C. Greubel, <a href="/A203430/b203430.txt">Table of n, a(n) for n = 1..40</a>
%t A203430 f[j_]:= j + Floor[j/2]; z = 20;
%t A203430 v[n_]:= Product[Product[f[k] - f[j], {j,k-1}], {k,2,n}]
%t A203430 d[n_]:= Product[(i-1)!, {i,n}]
%t A203430 Table[v[n], {n,z}]            (* this sequence *)
%t A203430 Table[v[n+1]/v[n], {n,z}]     (* A203431 *)
%t A203430 Table[v[n]/d[n], {n,z}]       (* A203432 *)
%o A203430 (Magma)
%o A203430 A203430:= func< n | n eq 1 select 1 else (&*[(&*[k-j+Floor((k+1)/2)-Floor((j+1)/2): j in [0..k-1]]) : k in [1..n-1]]) >;
%o A203430 [A203430(n): n in [1..25]]; // _G. C. Greubel_, Sep 27 2023
%o A203430 (SageMath)
%o A203430 def A203430(n): return product(product(k-j+((k+1)//2)-((j+1)//2) for j in range(k)) for k in range(1, n))
%o A203430 [A203430(n) for n in range(1, 31)] # _G. C. Greubel_, Sep 27 2023
%Y A203430 Cf. A032766, A203431, A203432.
%K A203430 nonn
%O A203430 1,2
%A A203430 _Clark Kimberling_, Jan 02 2012