A328001 T(n, k) = k!*(n-k)!/(floor(k/2)!*floor((n-k)/2)!)^2. Triangle read by rows, 0 <= k <= n.

1, 1, 1, 2, 1, 2, 6, 2, 2, 6, 6, 6, 4, 6, 6, 30, 6, 12, 12, 6, 30, 20, 30, 12, 36, 12, 30, 20, 140, 20, 60, 36, 36, 60, 20, 140, 70, 140, 40, 180, 36, 180, 40, 140, 70, 630, 70, 280, 120, 180, 180, 120, 280, 70, 630, 252, 630, 140, 840, 120, 900, 120, 840, 140, 630, 252

Offset

0,4

Links

Table of n, a(n) for n=0..65.

Formula

T(n, k) = s(k)*s(n-k) where s(n) = A056040(n).

Example

                               1;
                              1, 1;
                            2, 1, 2;
                           6, 2, 2, 6;
                         6, 6, 4, 6, 6;
                      30, 6, 12, 12, 6, 30;
                   20, 30, 12, 36, 12, 30, 20;
                140, 20, 60, 36, 36, 60, 20, 140;
             70, 140, 40, 180, 36, 180, 40, 140, 70;
         630, 70, 280, 120, 180, 180, 120, 280, 70, 630;

Maple

T := (n, k) -> k!*(n-k)!/(iquo(k, 2)!*iquo(n-k, 2)!)^2:
seq(seq(T(n, k), k=0..n), n=0..10);

Crossrefs

Row sums in A328000. Central column in A327998.

Cf. A056040.

Sequence in context: A152431 A143965 A182073 * A347563 A349269 A098361

Adjacent sequences: A327998 A327999 A328000 * A328002 A328003 A328004

Keyword

tabl,nonn

Author

Peter Luschny, Oct 01 2019

Status

approved