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Search: id:A131067
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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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+0
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; listen)
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OFFSET
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0,5
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COMMENT
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Row sums = A131068: (1, 2, 10, 32, 82, 188, 406,...), the binomial transform of (1, 1, 7, 7, 7,...).
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FORMULA
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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
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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
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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
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Cf. A109128, A131060, A131061, A131062, A131063, A131064, A131065, A131066, A131068.
Sequence in context: A021556 A109571 A133823 this_sequence A081581 A051425 A051469
Adjacent sequences: A131064 A131065 A131066 this_sequence A131068 A131069 A131070
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 13 2007
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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