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Search: id:A132117
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| A132117 |
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Binomial transform of [1, 7, 17, 17, 6, 0, 0, 0,...]. |
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+0
2
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| 1, 8, 32, 90, 205, 406, 728, 1212, 1905, 2860, 4136, 5798, 7917, 10570, 13840, 17816, 22593, 28272, 34960, 42770, 51821, 62238, 74152, 87700, 103025, 120276, 139608, 161182, 185165
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Let M = the infinite lower triangular matrix of the natural numbers: [1; 2,3; 4,5,6;...]; and V = [1, 2, 3,...]. Then M*V = A132117.
O.g.f.: -x(1+x)(2x+1)/(-1+x)^5. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2008
a(n) = (4*n+6*n^2+8*n^3+6*n^4)/24 [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 07 2008]
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EXAMPLE
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a(3) = 32 = (1, 2, 1) dot (1, 7, 17) = (1 + 14 + 17).
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MAPLE
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a := n -> (Matrix([[0, 0, 2, 13, 46]]). Matrix(5, (i, j)-> if (i=j-1) then 1 elif j=1 then [5, -10, 10, -5, 1][i] else 0 fi)^n)[1, 1] ; seq (a(n), n=1..29); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 07 2008]
a := n-> (4+(6+(8+6*n)*n)*n)*n/24; seq (a(n), n=1..29); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 07 2008]
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CROSSREFS
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Cf. A000027.
Sequence in context: A008412 A014819 A033155 this_sequence A159941 A053348 A019256
Adjacent sequences: A132114 A132115 A132116 this_sequence A132118 A132119 A132120
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 10 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 02 2008
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