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A125103
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Triangle read by rows: T(n,k)=binom(n,k)+2^k*binom(n,k+1) (0<=k<=n).
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1
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1, 2, 1, 3, 4, 1, 4, 9, 7, 1, 5, 16, 22, 12, 1, 6, 25, 50, 50, 21, 1, 7, 36, 95, 140, 111, 38, 1, 8, 49, 161, 315, 371, 245, 71, 1, 9, 64, 252, 616, 966, 952, 540, 136, 1, 10, 81, 372, 1092, 2142, 2814, 2388, 1188, 265, 1, 11, 100, 525, 1800, 4242, 6972, 7890, 5880
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums = A094374: (1, 3, 8, 21, 56,...)
Binomial transform of the infinite bidiagonal matrix with (1,1,1,...) in the main diagonal and (1,2,4,8,...) in the subdiagonal.
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EXAMPLE
| First few rows of the triangle are:
1;
2, 1;
3, 4, 1;
4, 9, 7, 1;
5, 16, 22, 12, 1;
6, 25, 50, 50, 21, 1;
7, 36, 95, 140, 111, 38, 1;
...
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MAPLE
| T:=(n, k)->binomial(n, k)+2^k*binomial(n, k+1): for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
| Cf. A094374.
Sequence in context: A103283 A104698 A067066 * A171275 A107616 A055208
Adjacent sequences: A125100 A125101 A125102 * A125104 A125105 A125106
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 20 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006
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