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Multi-level factorials: triangle with a(n,k)=a(n-1,k-1)*a(n-1,k) but with a(n,1)=n and a(n,n)=1.
2

%I #2 Mar 30 2012 18:51:35

%S 1,2,1,3,2,1,4,6,2,1,5,24,12,2,1,6,120,288,24,2,1,7,720,34560,6912,48,

%T 2,1,8,5040,24883200,238878720,331776,96,2,1,9,40320,125411328000,

%U 5944066965504000,79254226206720,31850496,192,2,1,10,362880

%N Multi-level factorials: triangle with a(n,k)=a(n-1,k-1)*a(n-1,k) but with a(n,1)=n and a(n,n)=1.

%e a(4,2)=a(3,1)*a(3,2)=3*2=6. Rows start 1; 2,1; 3,2,1; 4,6,2,1; ...

%Y Columns include A000027, A000142, A000178, A055462, A057527, A057528. Right hand side includes A000012, A007395, A007283. Cf. A066119.

%K nonn,tabl

%O 1,2

%A _Henry Bottomley_, Dec 05 2001