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A125100
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Triangle read by rows: T(n,k)=fibonacci(k+1)*binom(n,k)+(k+1)*binom(n,k+1) (0<=k<=n).
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1, 2, 1, 3, 4, 2, 4, 9, 9, 3, 5, 16, 24, 16, 5, 6, 25, 50, 50, 30, 8, 7, 36, 90, 120, 105, 54, 13, 8, 49, 147, 245, 280, 210, 98, 21, 9, 64, 224, 448, 630, 616, 420, 176, 34, 10, 81, 324, 756, 1260, 1512, 1344, 828, 315, 55, 11, 100, 450, 1200, 2310, 3276, 3570, 2880, 1620
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A081663: (1, 3, 9, 25, 66, 169...) is the binomial transform of A081659, (n + F(n+1).
Binomial transform of the bidiagonal matrix with the Fibonacci numbers (1,1,2,3,5,8...) in the main diagonal and (1,2,3...) in the subdiagonal. Sum of terms in row n = n*2^(n-1)+fibonacci(2n+1) (A081663).
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EXAMPLE
| First few rows of the triangle are:
1;
2, 1;
3, 4, 2;
4, 9, 9, 3;
5, 16, 24, 16, 5;
6, 25, 50, 50, 30, 8;
7, 36, 90, 120, 105, 54, 13;
8, 49, 147, 245, 280, 210, 98, 21;
...
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MAPLE
| with(combinat): T:=(n, k)->binomial(n, k)*fibonacci(k+1)+(k+1)*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. A081663, A081659.
Cf. A000045.
Sequence in context: A131389 A131394 A130585 * A128544 A120058 A102756
Adjacent sequences: A125097 A125098 A125099 * A125101 A125102 A125103
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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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