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Triangular array generated by its row sums: T(n,0)=1 for n >= 1, T(n,1)=r(n-1), T(n,k)=T(n,k-1)+r(n-k) for k=2,3,...,n, n >= 2, r(h)=sum of the numbers in row h of T.
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%I #7 Jun 13 2013 04:40:43

%S 1,1,1,1,2,3,1,6,8,9,1,24,30,32,33,1,120,144,150,152,153,1,720,840,

%T 864,870,872,873,1,5040,5760,5880,5904,5910,5912,5913,1,40320,45360,

%U 46080,46200,46224,46230,46232,46233,1,362880,403200

%N Triangular array generated by its row sums: T(n,0)=1 for n >= 1, T(n,1)=r(n-1), T(n,k)=T(n,k-1)+r(n-k) for k=2,3,...,n, n >= 2, r(h)=sum of the numbers in row h of T.

%e Rows:

%e 1;

%e 1,1;

%e 1,2,3;

%e 1,6,8,9;

%e 1,24,30,32,33;

%e 1,120,144,150,152,153;

%Y n-th row sum is A000142(n+1) = (n+1)!.

%Y T(n, n)=A007489(n) for n >= 1, T(n+1, 2)=A001048(n)

%K nonn,tabl,eigen

%O 0,5

%A _Clark Kimberling_