%I #8 Sep 08 2022 08:45:45

%S 1,1,3,15,35,315,693,9009,19305,328185,692835,14549535,30421755,

%T 760543875,1579591125,45808142625,94670161425,3124115327025,

%U 6432002143875,237984079323375,488493636505875,20028239096740875

%N Sequence related to the column sums of the BG2 matrix

%H G. C. Greubel, <a href="/A161738/b161738.txt">Table of n, a(n) for n = 1..667</a>

%F a(n) = product((2*n-3-2*k), k=0..floor(n/2-1)).

%F numer(a(n+2)/a(n+1)) = A005408(n) for n=>0.

%F denom(a(n+2)/a(n+1)) = A093178(n) for n=>0.

%t Table[Product[(2*n - 3 - 2*k), {k, 0, Floor[n/2 - 1]}], {n, 1, 50}] (* _G. C. Greubel_, Sep 26 2018 *)

%o (PARI) for(n=1,50, print1(prod(k=0,floor(n/2 -1), 2*n-2*k-3), ", ")) \\ _G. C. Greubel_, Sep 26 2018

%o (Magma) [1] cat [(&*[2*n-2*k-3:k in [0..Floor(n/2 -1)]]): n in [2..50]]; // _G. C. Greubel_, Sep 26 2018

%Y Cf. A161736, A005408 and A093178.

%K easy,nonn

%O 1,3

%A _Johannes W. Meijer_, Jun 18 2009