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

0,5

Comments

A125231 is another triangle with the same row sums A045623: (1, 2, 5, 12, 28, 64, 144, 320...).

Links

Table of n, a(n) for n=0..72.

Formula

T(n,k) = Sum_{j=k..min(2*k,n)} C(n,j).

Example

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

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);

Crossrefs

Cf. A007318, A125231. Columns k=0-3 give: A000012, A000217, A006522(n+1), A055796(n-3). Row sums give: A045623.

Sequence in context: A133567 A271665 A184049 * A208334 A162430 A305059

Adjacent sequences: A125227 A125228 A125229 * A125231 A125232 A125233

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 24 2006

Extensions

Edited with more terms and Maple program by Alois P. Heinz, Oct 16 2009

Status

approved