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A016095
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Triangular array T(n,k) read by rows, where T(n,k) = coefficient of x^n*y^k in 1/(1-x-y-(x+y)^2).
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7
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1, 1, 1, 2, 4, 2, 3, 9, 9, 3, 5, 20, 30, 20, 5, 8, 40, 80, 80, 40, 8, 13, 78, 195, 260, 195, 78, 13, 21, 147, 441, 735, 735, 441, 147, 21, 34, 272, 952, 1904, 2380, 1904, 952, 272, 34, 55, 495, 1980, 4620, 6930, 6930, 4620, 1980, 495, 55
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Triangle T(n,k), 0<=k<=n, read by rows, given by [1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - DELEHAM Philippe (kolotoko(aT)lagoon.nc), Aug 10 2005
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FORMULA
| G.f.: 1/(1-x-y-(x+y)^2).
T(n,k)=Fib(n+1)*binomial(n,k)=A000045(n+1)*A007318(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 14 2006
Sum_[k, 0<=k<=[n/2]}T(n-k,k)=A123392(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 14 2006
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MAPLE
| read transforms; 1/(1-x-y-(x+y)^2); SERIES2(%, x, y, 12); SERIES2TOLIST(%, x, y, 12);
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CROSSREFS
| Columns include A000045, A023607. Central diagonal is A102307. Antidiagonal sums are in A063727.
Sequence in context: A151849 A141387 A134400 * A181399 A165464 A158137
Adjacent sequences: A016092 A016093 A016094 * A016096 A016097 A016098
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 23 2001
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