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A242653
Triangle read by rows: T(n,k) = ((n+k)/2)!/k! if n,k have same parity, otherwise 0.
1
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
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
KEYWORD
nonn,tabl,easy
AUTHOR
N. J. A. Sloane, May 29 2014
STATUS
approved