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A131067
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Triangle read by rows: T(n,k)=7*binom(n,k)-6 (0<=k<=n).
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2
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1, 1, 1, 1, 8, 1, 1, 15, 15, 1, 1, 22, 36, 22, 1, 1, 29, 64, 64, 29, 1, 1, 36, 99, 134, 99, 36, 1, 1, 43, 141, 239, 239, 141, 43, 1, 1, 50, 190, 386, 484, 386, 190, 50, 1, 1, 57, 246, 582, 876, 876, 582, 246, 57, 1, 1, 64, 309, 834, 1464, 1758, 1464, 834, 309, 64, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums = A131068: (1, 2, 10, 32, 82, 188, 406,...), the binomial transform of (1, 1, 7, 7, 7,...).
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FORMULA
| G.f.=G(t,z)=(1-z-tz+7tz^2)/[(1-z)(1-tz)(1-z-tz)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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EXAMPLE
| First few rows of the triangle are:
1;
1, 1;
1, 8, 1;
1, 15, 15, 1;
1, 22, 36, 22, 1;
1, 29, 64, 64, 29, 1;
...
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MAPLE
| T := proc (n, k) if k <= n then 7*binomial(n, k)-6 else 0 end if end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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CROSSREFS
| Cf. A109128, A131060, A131061, A131062, A131063, A131064, A131065, A131066, A131068.
Sequence in context: A146881 A174301 A174378 * A157170 A143679 A081581
Adjacent sequences: A131064 A131065 A131066 * A131068 A131069 A131070
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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