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Ceiling(Gamma(n/4)).
2

%I #6 Apr 17 2017 22:45:57

%S 4,2,2,1,1,1,1,1,2,2,2,2,3,4,5,6,9,12,17,24,36,53,79,120,185,288,454,

%T 720,1156,1872,3058,5040,8377,14035,23699,40320,69107,119293,207359,

%U 362880,639233,1133279,2021747,3628800,6552135,11899424,21733774,39916800

%N Ceiling(Gamma(n/4)).

%C There are three integer-valued interpolations between successive factorials.

%H Clark Kimberling, <a href="/A285001/b285001.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = ceiling(Gamma(n/4)).

%t Table[Ceiling[Gamma[n/4]], {n, 1, 35}]

%o (PARI) a(n) = ceil(gamma(n/4)); \\ _Michel Marcus_, Apr 17 2017

%Y Cf. A000142, A285000.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Apr 17 2017