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Search: id:A122031
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| A122031 |
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a(n) = a(n - 1) + (n - 1)*a(n - 2). |
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+0
1
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| 1, 2, 3, 7, 16, 44, 124, 388, 1256, 4360, 15664, 59264, 231568, 942736, 3953120, 17151424, 76448224, 350871008, 1650490816, 7966168960, 39325494464, 198648873664, 1024484257408, 5394759478016, 28957897398400
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 13 2009: (Start)
Equals the eigensequence of an infinite lower triangular matrix with
(1, 1, 1,...) in the main diagaonal, (1, 1, 2, 3, 4, 5,...) in the subdiagonal
and the rest zeros. (End)
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FORMULA
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Paul Abbott (paul(AT)physics.uwa.edu.au) gives a generating function: Needs["DiscreteMath`RSolve`"]; ExponentialGeneratingFunction[{a[0] == 1, a[1] == 2, a[n] == a[n - 1] + (n - 1)*a[n - 2]}, a[n], n, z] f[z_]=(1/2)*Exponential[z + z^2/2]*(2 - Sqrt[2E pi ] Erf[1/Sqrt[2]] + Sqrt[2E pi ] Erf[(1 + z)/Sqrt[2]])
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MATHEMATICA
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a[0] = 1; a[1] = 2; a[n_] := a[n] = a[n - 1] + (n - 1)*a[n - 2] Table[a[n], {n, 0, 30}]
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CROSSREFS
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Cf. A000898, A121966, A062267, A122021, A122022.
Sequence in context: A091487 A162092 A143884 this_sequence A089125 A002854 A036356
Adjacent sequences: A122028 A122029 A122030 this_sequence A122032 A122033 A122034
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 13 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 17 2006
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