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A139488
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Binomial transform of [1, 2, 3, 4, 0, 0, 0,...].
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0
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1, 3, 8, 20, 43, 81, 138, 218, 325, 463, 636, 848, 1103, 1405, 1758, 2166, 2633, 3163, 3760, 4428, 5171, 5993, 6898, 7890, 8973, 10151, 11428, 12808, 14295, 15893, 17606, 19438, 21393, 23475, 25688, 28036, 30523, 33153, 35930, 38858, 41941, 45183
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A104249 = binomial transform of [1, 2, 3, 0, 0, 0,...].
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FORMULA
| A007318 * [1, 2, 3, 4, 0, 0, 0,...].
a(n)=(4n^3-3n^2+11n+6)/6. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 30 2008
G.f.: (1-x+2*x^2+2*x^3)/(1-x)^4. [Colin Barker, Feb 01 2012]
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EXAMPLE
| a(5) = 43 = (1, 4, 6, 4, 1) dot (1, 2, 3, 4, 0) = (1 + 8, + 18 + 16 + 0).
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MAPLE
| a:=proc(n) options operator, arrow: (2/3)*n^3-(1/2)*n^2+(11/6)*n+1 end proc: seq(a(n), n=0..35); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 30 2008
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MATHEMATICA
| f[n_] := Plus @@ (Table[ Binomial[n - 1, i], {i, 0, n - 1}] PadRight[{1, 2, 3, 4}, n]); Array[f, 43] - Robert G. Wilson v, (rgwv(AT)rgwv.com), Apr 24 2008
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CROSSREFS
| Cf. A005408, A104249.
Sequence in context: A143785 A182735 A135565 * A028307 A027298 A000236
Adjacent sequences: A139485 A139486 A139487 * A139489 A139490 A139491
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KEYWORD
| nonn,changed
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2008
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 24 2008
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