A268363 Number of n X 2 arrays containing 2 copies of 0..n-1 with row sums equal.

1, 1, 4, 12, 96, 480, 5760, 40320, 645120, 5806080, 116121600, 1277337600, 30656102400, 398529331200, 11158821273600, 167382319104000, 5356234211328000, 91055981592576000, 3278015337332736000, 62282291409321984000, 2491291656372879360000

Offset

0,3

Comments

Column 2 of A268367.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..425 (terms n = 1..25 from R. H. Hardin)

Formula

a(n) = 2^floor(n/2) * n!. - Joel B. Lewis, Aug 11 2016

a(2n) = A065140(n) for terms > a(1) - Terry D. Grant, May 28 2017

a(n) = A158867(n, n) for n > 0. - G. C. Greubel, Mar 08 2022

Example

Some solutions for n=5
..3..1....1..3....4..0....0..4....0..4....4..0....4..0....4..0....2..2....1..3
..1..3....2..2....3..1....3..1....2..2....3..1....1..3....2..2....0..4....0..4
..0..4....0..4....0..4....2..2....1..3....1..3....0..4....1..3....3..1....4..0
..0..4....0..4....2..2....1..3....4..0....0..4....2..2....0..4....4..0....3..1
..2..2....3..1....1..3....0..4....1..3....2..2....1..3....3..1....3..1....2..2

Mathematica

Table[2^Floor[n/2] n!, {n, 0, 25}] (* Michael De Vlieger, Aug 11 2016 *)

Prog

(Magma) [2^Floor(n/2)*Factorial(n): n in [0..25]]; // G. C. Greubel, Mar 08 2022
(Sage) [2^(n//2)*factorial(n) for n in (0..25)] # G. C. Greubel, Mar 08 2022

Crossrefs

Cf. A065140, A121627, A268367.

Cf. A158867.

Sequence in context: A074930 A287596 A364901 * A377531 A038053 A217155

Adjacent sequences: A268360 A268361 A268362 * A268364 A268365 A268366

Keyword

nonn

Author

R. H. Hardin, Feb 03 2016

Extensions

Title clarified by Joel B. Lewis, Aug 11 2016

a(0)=1 prepended by Alois P. Heinz, May 27 2017

Status

approved