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a(n) = binomial(n - 1, ceiling(n/2)) * binomial(n - 1, ceiling(n/2) - 1).
0

%I #29 Dec 15 2024 05:26:59

%S 1,0,1,2,9,24,100,300,1225,3920,15876,52920,213444,731808,2944656,

%T 10306296,41409225,147232800,590976100,2127513960,8533694884,

%U 31031617760,124408576656,456164781072,1828114918084,6749962774464,27043120090000,100445874620000,402335398890000

%N a(n) = binomial(n - 1, ceiling(n/2)) * binomial(n - 1, ceiling(n/2) - 1).

%H Paolo Xausa, <a href="/A378070/b378070.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = binomial(n - 1, floor(n/2) - 1) * binomial(n - 1, ceiling(n/2) - 1).

%p a := n -> binomial(n-1, floor((n+1)/2))*binomial(n-1, floor((n+1)/2)-1);

%p seq(a(n), n = 0..27);

%t A378070[n_] := Binomial[n - 1, #]*Binomial[n - 1, # - 1] & [Ceiling[n/2]];

%t Array[A378070, 30, 0] (* _Paolo Xausa_, Dec 14 2024 *)

%Y Cf. A007318, A060150 (even bisection), A135389 (odd bisection), A378060.

%K nonn,easy,new

%O 0,4

%A _Peter Luschny_, Dec 13 2024