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A125026
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Triangle read by rows: T(n,k)=k*binom(n,k) + binom(n-1,k) (1<=k<=n).
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0
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1, 3, 2, 5, 7, 3, 7, 15, 13, 4, 9, 26, 34, 21, 5, 11, 40, 70, 65, 31, 6, 13, 57, 125, 155, 111, 43, 7, 15, 77, 203, 315, 301, 175, 57, 8, 17, 100, 308, 574, 686, 532, 260, 73, 9, 19, 126, 444, 966, 1386, 1344, 876, 369, 91, 10, 21, 155, 615, 1530, 2562, 2982, 2430, 1365
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums = (1, 5, 15, 39, 95...): A099035, = (n+1)*2^(n-1) - 1.
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EXAMPLE
| First few rows of the triangle are:
1;
3, 2;
5, 7, 3;
7, 15, 13, 4;
9, 26, 34, 21, 5;
11, 40, 70, 65, 31, 6;
13, 57, 125, 155, 111, 43, 7;
...
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MAPLE
| T:=(n, k)->k*binomial(n, k)+binomial(n-1, k): for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
| Cf. A099035.
Sequence in context: A181883 A021311 A128224 * A130295 A006369 A097284
Adjacent sequences: A125023 A125024 A125025 * A125027 A125028 A125029
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 15 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006
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