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

0,8

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.

Example

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
...

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 *)

Crossrefs

Sequence in context: A322378 A053121 A113408 * A191530 A321435 A173863

Adjacent sequences: A242650 A242651 A242652 * A242654 A242655 A242656

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, May 29 2014

Status

approved