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a(n) = ceiling(Gamma(n/2)).
2

%I #12 Jul 27 2024 03:52:38

%S 2,1,1,1,2,2,4,6,12,24,53,120,288,720,1872,5040,14035,40320,119293,

%T 362880,1133279,3628800,11899424,39916800,136843366,479001600,

%U 1710542069,6227020800,23092317923,87178291200,334838609874,1307674368000,5189998453041

%N a(n) = ceiling(Gamma(n/2)).

%C The bisections are A000142 (factorials) and 1+A014510.

%H Clark Kimberling, <a href="/A284995/b284995.txt">Table of n, a(n) for n = 1..500</a>

%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[Ceiling[Gamma[n/2]], {n, 1, 35}]

%Y Cf. A000142, A014510, A284994.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Apr 08 2017