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Triangle of the divisors of the coefficients of triangles A138771 and A165675
3

%I #5 Feb 01 2015 02:00:45

%S 1,1,1,1,1,1,1,1,1,2,1,1,1,2,6,1,1,1,2,6,24,1,1,1,2,6,24,120,1,1,1,2,

%T 6,24,120,720,1,1,1,2,6,24,120,720,5040,1,1,1,2,6,24,120,720,5040,

%U 40320,1,1,1,2,6,24,120,720,5040,40320,362880

%N Triangle of the divisors of the coefficients of triangles A138771 and A165675

%F a(n) = A138771(n)/A165675(n-1).

%e Triangle starts:

%e 1,

%e 1, 1,

%e 1, 1, 1,

%e 1, 1, 1, 2,

%e 1, 1, 1, 2, 6,

%e 1, 1, 1, 2, 6, 24,

%e 1, 1, 1, 2, 6, 24, 120,

%e 1, 1, 1, 2, 6, 24, 120, 720,

%e 1, 1, 1, 2, 6, 24, 120, 720, 5040,

%e 1, 1, 1, 2, 6, 24, 120, 720, 5040, 40320,

%e 1, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880,

%e ...

%p nmax:=11: for n from 1 to nmax do a(n,1):=1 od: for n from 2 to nmax do for m from 2 to n do a(n,m):=(m-2)! od: od: for n from 1 to nmax do seq(a(n,m),m=1..n) od;

%Y Cf. A138771, A165675 and A000142.

%Y A000012 (3x), A007395, A010722, A010863 equal the first six left hand columns.

%Y A159333 equals, for n=>-1, all right hand columns.

%Y A067078 equals the row sums.

%K easy,nonn,tabl

%O 1,10

%A _Johannes W. Meijer_, Oct 05 2009