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A125230
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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.
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1
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| A125231 is another triangle with the same row sums A045623: (1, 2, 5, 12, 28, 64, 144, 320...).
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FORMULA
| T(n,k) = Sum_{j=k..min(2*k,n)} C(n,j).
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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
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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);
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CROSSREFS
| Cf. A007318, A125231. Columns k=0-3 give: A000012, A000217, A006522(n+1), A055796(n-3). Row sums give: A045623.
Sequence in context: A067433 A133567 A184049 * A162430 A128101 A124802
Adjacent sequences: A125227 A125228 A125229 * A125231 A125232 A125233
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 24 2006
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EXTENSIONS
| Edited with more terms and Maple program by Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 16 2009
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