A242653 Triangle read by rows: T(n,k) = ((n+k)/2)!/k! if n,k have same parity, otherwise 0.

1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0, 3, 0, 1, 0, 6, 0, 4, 0, 1, 6, 0, 12, 0, 5, 0, 1, 0, 24, 0, 20, 0, 6, 0, 1, 24, 0, 60, 0, 30, 0, 7, 0, 1, 0, 120, 0, 120, 0, 42, 0, 8, 0, 1, 120, 0, 360, 0, 210, 0, 56, 0, 9, 0, 1, 0, 720, 0, 840, 0, 336, 0, 72, 0, 10, 0, 1, 720, 0, 2520, 0, 1680, 0, 504, 0, 90, 0, 11, 0, 1

Offset: 0

Author

N. J. A. Sloane, May 29 2014

Keywords

• nonn
• tabl
• easy

Examples

			Triangle begins:
  1
  0  1
  1  0  1
  0  2  0  1
  2  0  3  0 1
  0  6  0  4 0 1
  6  0 12  0 5 0 1
  0 24  0 20 0 6 0 1
  ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10010
• Alexander Kreinin, Combinatorial Properties of Mills' Ratio, arXiv:1405.5852, 2014. See Table 4.

Crossrefs

Cf. A122851.

Programs

Maple

N:= 1000; # to get a(0) to a(N)
count:= -1;
for n from 0 while count < N do
  for k from 0 to n while count  < N do
    count:= count+1;
    if type(n-k,even) then
       A[count]:= ((n+k)/2)!/k!
    else
       A[count]:= 0
    fi;
  od
od:
seq(A[i],i=0..N); # Robert Israel, Jun 10 2014

Mathematica

Table[If[EvenQ[n-k], ((n+k)/2)!/k!, 0], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 19 2018 *)