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a(n) = n! / floor(n/3)!.
4

%I #12 Jul 22 2022 10:13:39

%S 1,1,2,6,24,120,360,2520,20160,60480,604800,6652800,19958400,

%T 259459200,3632428800,10897286400,174356582400,2964061900800,

%U 8892185702400,168951528345600,3379030566912000,10137091700736000,223016017416192000,5129368400572416000

%N a(n) = n! / floor(n/3)!.

%F E.g.f.: (1 - x^3) * exp(x^3)/(1 - x).

%t a[n_] := n!/Floor[n/3]!; Array[a, 24, 0] (* _Amiram Eldar_, Jul 22 2022 *)

%o (PARI) a(n) = n!/(n\3)!;

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^3)*exp(x^3)/(1-x)))

%Y Cf. A081125, A355990.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Jul 22 2022