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Triangular array generated by its row sums: T(n,0)=1 for n >= 0, T(1,1)=2, T(n,k)=T(n,k-1)+d*r(n-k) for k=2,3,...,n, d=(-1)^(k+1), n >= 2, r(h)=sum of the numbers in row h of T.
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%I #4 Mar 30 2012 18:57:02

%S 1,1,2,1,3,2,1,6,3,4,1,14,8,11,10,1,44,30,36,33,34,1,178,134,148,142,

%T 145,144,1,892,714,758,744,750,747,748,1,5354,4462,4640,4596,4610,

%U 4604,4607,4606,1,37480,32126,33018,32840,32884,32870

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

%e Rows: {1}, {1,2}, {1,3,2}, {1,6,3,4}, ...

%K nonn,tabl,eigen

%O 1,3

%A _Clark Kimberling_