|
%I #43 Mar 08 2022 19:33:55
%S 1,1,4,12,96,480,5760,40320,645120,5806080,116121600,1277337600,
%T 30656102400,398529331200,11158821273600,167382319104000,
%U 5356234211328000,91055981592576000,3278015337332736000,62282291409321984000,2491291656372879360000
%N Number of n X 2 arrays containing 2 copies of 0..n-1 with row sums equal.
%C Column 2 of A268367.
%H Alois P. Heinz, <a href="/A268363/b268363.txt">Table of n, a(n) for n = 0..425</a> (terms n = 1..25 from R. H. Hardin)
%F a(n) = 2^floor(n/2) * n!. - _Joel B. Lewis_, Aug 11 2016
%F a(2n) = A065140(n) for terms > a(1) - _Terry D. Grant_, May 28 2017
%F a(n) = A158867(n, n) for n > 0. - _G. C. Greubel_, Mar 08 2022
%e Some solutions for n=5
%e ..3..1....1..3....4..0....0..4....0..4....4..0....4..0....4..0....2..2....1..3
%e ..1..3....2..2....3..1....3..1....2..2....3..1....1..3....2..2....0..4....0..4
%e ..0..4....0..4....0..4....2..2....1..3....1..3....0..4....1..3....3..1....4..0
%e ..0..4....0..4....2..2....1..3....4..0....0..4....2..2....0..4....4..0....3..1
%e ..2..2....3..1....1..3....0..4....1..3....2..2....1..3....3..1....3..1....2..2
%t Table[2^Floor[n/2] n!, {n,0,25}] (* _Michael De Vlieger_, Aug 11 2016 *)
%o (Magma) [2^Floor(n/2)*Factorial(n): n in [0..25]]; // _G. C. Greubel_, Mar 08 2022
%o (Sage) [2^(n//2)*factorial(n) for n in (0..25)] # _G. C. Greubel_, Mar 08 2022
%Y Cf. A065140, A121627, A268367.
%Y Cf. A158867.
%K nonn
%O 0,3
%A _R. H. Hardin_, Feb 03 2016
%E Title clarified by _Joel B. Lewis_, Aug 11 2016
%E a(0)=1 prepended by _Alois P. Heinz_, May 27 2017
| 