A357013 Triangle read by rows. T(n, k) = ((2*n)! * k!) / (n + k)!.

1, 2, 1, 12, 4, 2, 120, 30, 12, 6, 1680, 336, 112, 48, 24, 30240, 5040, 1440, 540, 240, 120, 665280, 95040, 23760, 7920, 3168, 1440, 720, 17297280, 2162160, 480480, 144144, 52416, 21840, 10080, 5040, 518918400, 57657600, 11531520, 3144960, 1048320, 403200, 172800, 80640, 40320

Offset

0,2

Links

Table of n, a(n) for n=0..44.

Example

[0]        1;
[1]        2,       1;
[2]       12,       4,      2;
[3]      120,      30,     12,      6;
[4]     1680,     336,    112,     48,    24;
[5]    30240,    5040,   1440,    540,   240,   120;
[6]   665280,   95040,  23760,   7920,  3168,  1440,   720;
[7] 17297280, 2162160, 480480, 144144, 52416, 21840, 10080, 5040;

Maple

T := (n, k) -> ((2*n)! * k!) / (n + k)!:
for n from 0 to 6 do seq(T(n, k), k = 0..n) od;

Crossrefs

Cf. A001813 (column 0), A000142 (main diagonal).

Sequence in context: A286640 A288359 A107722 * A370552 A167128 A332749

Adjacent sequences: A357010 A357011 A357012 * A357014 A357015 A357016

Keyword

nonn,tabl

Author

Peter Luschny, Sep 25 2022

Status

approved