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%I #13 Aug 04 2024 20:46:10
%S 1,3,9,36,180,1260,12600,189000,4347000,156492000,8920044000,
%T 811724004000,118511704584000,27850250577240000,10555244968773960000,
%U 6459809920889663520000,6388752011759877221280000,10215614466804043676826720000,26417579011155256948273897920000
%N a(n) = (1/2)*Product_{k=0..n} (F(k)+2), where F=A000045 (Fibonacci numbers).
%C a(n+1)/a(n) is an integer for n>=0, so (a(n)) is a divisibility sequence.
%t q[n_] := Fibonacci[n]
%t p[n_] := Product[q[k] + 2, {k, 0, n}]
%t Table[Simplify[p[n]/2], {n, 0, 20}]
%o (PARI) a(n) = prod(k=0, n, fibonacci(k)+2)/2; \\ _Michel Marcus_, Aug 04 2024
%Y Cf. A000045, A082480.
%K nonn
%O 0,2
%A _Clark Kimberling_, Aug 03 2024