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Search: id:A123029
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| A123029 |
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A000045 inside a second linear differential equation recursion: b(n)=b(n-1)+b(n-2)-->Binet[n] of A000045 a(n)=b(n)*a[n-2]/(n*(n-1)). |
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1
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| 1, 1, 1, 2, 3, 10, 24, 130, 504, 4420, 27720, 393380, 3991680, 91657540, 1504863360, 55911099400, 1485300136320, 89290025741800, 3838015552250880, 373321597626465800, 25964175210977203200, 4086378207619294646800
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Using the solutions to these second order differenential equations Markov/ linear recursions can be encoded as analog functions.
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FORMULA
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b(n)=b(n-1)+b(n-2)-->Binet[n] of Fibonacci a(n)=b(n)*a[n-2]/(n*(n-1)) Output=a(n)*n!
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MATHEMATICA
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f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == a[n - 1] + a[n - 2], a[0] == 0, a[1] == 1}, a[n], n][[1]] // FullSimplify] ; Clear[a] a[n_] := a[n] = f[n]*a[n - 2]/(n*(n - 1)); a[0] = 1; a[1] = 1; Table[ExpandAll[a[n]*n! ], {n, 0, 30}]
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CROSSREFS
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Cf. A000045.
Sequence in context: A130002 A105286 A059929 this_sequence A103018 A005158 A005225
Adjacent sequences: A123026 A123027 A123028 this_sequence A123030 A123031 A123032
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 25 2006
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