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.
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, 28, 91, 98, 64, 29, 8, 1, 1, 36, 154, 210, 163, 93, 37, 9, 1, 1, 45, 246, 420, 381, 256, 130, 46, 10, 1, 1, 55, 375, 792, 837, 638, 386, 176, 56, 11, 1, 1, 66, 550, 1419, 1749, 1485, 1024
Offset: 0
Examples
T(5,2) = C(5,2) + C(5,3) + C(5,4) = 10 + 10 + 5 = 25. First few rows of the triangle are: 1 1 1 1 3 1 1 6 4 1 1 10 11 5 1 1 15 25 16 6 1
Crossrefs
Programs
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Maple
T:= (n, k)-> add (binomial (n, j), j=k..min(2*k, n)): seq (seq (T(n, k), k=0..n), n=0..12);
Formula
T(n,k) = Sum_{j=k..min(2*k,n)} C(n,j).
Extensions
Edited with more terms and Maple program by Alois P. Heinz, Oct 16 2009
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