A161738 Sequence related to the column sums of the BG2 matrix.

1, 1, 3, 15, 35, 315, 693, 9009, 19305, 328185, 692835, 14549535, 30421755, 760543875, 1579591125, 45808142625, 94670161425, 3124115327025, 6432002143875, 237984079323375, 488493636505875, 20028239096740875

Offset: 1

Author

Johannes W. Meijer, Jun 18 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..667

Crossrefs

Cf. A161736, A005408 and A093178.

Programs

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

Mathematica

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

PARI

for(n=1,50, print1(prod(k=0,floor(n/2 -1), 2*n-2*k-3), ", ")) \\ G. C. Greubel, Sep 26 2018

Formula

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

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

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