A203533 - OEIS

%I #13 Jan 13 2025 15:06:19

%S 1,10,840,464100,1481407200,32851686067200,5186361382800998400,

%T 4436556151786001058816000,19667253420867342693731328000000,

%U 605862171333980479840975997239296000000,132207384898194165523202154782408753283072000000

%N a(n) = A203530(n)/A000178(n-1); A000178 = (superfactorials).

%C It is conjectured that every term is an integer.

%t t = Table[If[PrimeQ[k], 0, k], {k, 1, 100}];

%t composite = Rest[Rest[Union[t]]]       (* A002808 *)

%t f[j_] := composite[[j]]; z = 20;

%t v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]

%t d[n_] := Product[(i - 1)!, {i, 1, n}]  (* A000178 *)

%t Table[v[n], {n, 1, z}]                 (* A203530 *)

%t Table[v[n + 1]/v[n], {n, 1, z - 1}]    (* A203532 *)

%t Table[v[n]/d[n], {n, 1, 20}]           (* A203533 *)

%Y Cf. A000178, A203530, A203532, A002808, A093883, A203420.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 03 2012