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Floor(Gamma(n/2)).
2

%I #11 Jul 27 2024 03:53:05

%S 1,1,0,1,1,2,3,6,11,24,52,120,287,720,1871,5040,14034,40320,119292,

%T 362880,1133278,3628800,11899423,39916800,136843365,479001600,

%U 1710542068,6227020800,23092317922,87178291200,334838609873,1307674368000,5189998453040

%N Floor(Gamma(n/2)).

%C The bisections are A000142 (factorials) and A014510.

%H Clark Kimberling, <a href="/A284994/b284994.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = floor(Gamma(n/2)).

%e Let s = sqrt(Pi); for n>=1, gamma(n/2) takes the values s, 1, s/2, 1, 3s/4, 2, 15s/8, 6, so that a(n) begins with 1,1,0,1,1,2,3,6.

%t Table[Floor[Gamma[n/2]], {n, 1, 35}]

%Y Cf. A000142, A014510, A284995.

%K nonn,easy

%O 1,6

%A _Clark Kimberling_, Apr 08 2017