A378070 a(n) = binomial(n - 1, ceiling(n/2)) * binomial(n - 1, ceiling(n/2) - 1).

1, 0, 1, 2, 9, 24, 100, 300, 1225, 3920, 15876, 52920, 213444, 731808, 2944656, 10306296, 41409225, 147232800, 590976100, 2127513960, 8533694884, 31031617760, 124408576656, 456164781072, 1828114918084, 6749962774464, 27043120090000, 100445874620000, 402335398890000

Offset: 0

Author

Peter Luschny, Dec 13 2024

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000

Crossrefs

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

Programs

Maple

a :=  n -> binomial(n-1, floor((n+1)/2))*binomial(n-1, floor((n+1)/2)-1);
seq(a(n), n = 0..27);

Mathematica

A378070[n_] := Binomial[n - 1, #]*Binomial[n - 1, # - 1] & [Ceiling[n/2]];
Array[A378070, 30, 0] (* Paolo Xausa, Dec 14 2024 *)

Formula

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