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A125230 Triangle T(n,k) (0<=k<=n) read by rows in which column k contains the binomial transform of the sequence of k 0's, (k+1) 1's, followed by 0's.

%I A125230 #5 Mar 30 2012 17:37:22
%S A125230 1,1,1,1,3,1,1,6,4,1,1,10,11,5,1,1,15,25,16,6,1,1,21,50,42,22,7,1,1,
%T A125230 28,91,98,64,29,8,1,1,36,154,210,163,93,37,9,1,1,45,246,420,381,256,
%U A125230 130,46,10,1,1,55,375,792,837,638,386,176,56,11,1,1,66,550,1419,1749,1485,1024
%N A125230 Triangle T(n,k) (0<=k<=n) read by rows in which column k contains the binomial transform of the sequence of k 0's, (k+1) 1's, followed by 0's.
%C A125230 A125231 is another triangle with the same row sums A045623: (1, 2, 5, 12, 28, 64, 144, 320...).
%F A125230 T(n,k) = Sum_{j=k..min(2*k,n)} C(n,j).
%e A125230 T(5,2) = C(5,2) + C(5,3) + C(5,4) = 10 + 10 + 5 = 25.
%e A125230 First few rows of the triangle are:
%e A125230 1
%e A125230 1 1
%e A125230 1 3 1
%e A125230 1 6 4 1
%e A125230 1 10 11 5 1
%e A125230 1 15 25 16 6 1
%p A125230 T:= (n, k)-> add (binomial (n, j), j=k..min(2*k, n)): seq (seq (T(n, k), k=0..n), n=0..12);
%Y A125230 Cf. A007318, A125231. Columns k=0-3 give: A000012, A000217, A006522(n+1), A055796(n-3). Row sums give: A045623.
%K A125230 nonn,tabl
%O A125230 0,5
%A A125230 _Gary W. Adamson_, Nov 24 2006
%E A125230 Edited with more terms and Maple program by _Alois P. Heinz_, Oct 16 2009