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Search: id:A075887
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| A075887 |
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a(n) = 1 + n + n[n/2] + n[n/2][n/3] +... + n[n/2][n/3]...[n/n], where [x]=ceil(x). |
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+0
1
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| 1, 2, 5, 16, 45, 171, 421, 1968, 4553, 19225, 57261, 226854, 496309, 3136420, 6764563, 24850336, 84877201, 380461599, 805949533, 4411165990, 9288196621, 48275465722, 154143694937, 527401107276, 1100708161081, 8151403215501
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) ~ L^n where L = 3.517486, ln(L) = sum_{k=1..inf} ln(k+1)/[k(k+1)] = 1.257746
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FORMULA
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a(n) = 1 + sum_{m=1..n} product_{k=1..m} ceil(n/k) for n>0, and a(0)=1.
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EXAMPLE
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a(5) = 171 = 1 +5[5/2] +5[5/2][5/3] +5[5/2][5/3][5/4] +5[5/2][5/3][5/4][5/5] = 1 + 5 + 5*3 + 5*3*2 + 5*3*2*2 + 5*3*2*2*1, here [x]=ceil(x).
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CROSSREFS
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Sequence in context: A102866 A132734 A138573 this_sequence A005497 A118973 A121651
Adjacent sequences: A075884 A075885 A075886 this_sequence A075888 A075889 A075890
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KEYWORD
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easy,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 17 2002
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