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A095989
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INVERTi transform applied to the ordered Bell numbers.
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3
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1, 2, 8, 48, 368, 3376, 35824, 430512, 5773936, 85482032, 1384936688, 24380214960, 463522810736, 9468048895792, 206831329017328, 4812581925690288, 118843801816575088, 3104590192664327216, 85544737118902122224
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A set composition of n is an ordered sequence [S_1, S_2, ..., S_k] where S_i subset of [n] all disjoint and the union of all S_i is [n] (see A000670). A set composition is atomic if S_1 union ... union S_j does not equal [r] for any r<n and j<k. a(n) is the number of atomic set compositions.
A preference function of n is a word of length n where all the numbers 1 through k occur at least once for some k<=n (see A000670). A preference function is atomic if no strict leading subword contains the only occurrences in the word of the letters 1 through j<k. a(n) is the number of atomic preference functions.
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FORMULA
| G.f.: 1-1/sum( A000670(k)*q^k, k >= 0)
G.f.: x/(1-2x/(1-2x/(1-4x/(1-3x/(1-6x/(1-4x/(1-8x/(1-5x/(1-...(continued fraction). - From DELEHAM Philippe, Nov 22 2011
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EXAMPLE
| atomic set compositions a(1)=1: [{1}]; a(2)=2: [{12}], [{2},{1}]; a(3)=8: [{123}], [{2},{13}], [{3}, {12}], [{23}, {1}], [{13},{2}], [{2},{3},{1}], [{3},{1},{2}], [{3},{2},{1}]
atomic preference functions a(1) = 1: 1; a(2)=2: 11, 21; a(3)=8: 111, 212, 221, 211, 121, 312, 231, 321
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MAPLE
| A000670 := proc(n) option remember; local k; if n <=1 then 1 else add(binomial(n, k)*A000670(n-k), k=1..n); fi; end: add(A000670(k)*x^k, k=0..20): series(1-1/%, x, 21): [seq(coeff(%, x, i), i=1..20)];
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CROSSREFS
| Cf. A000670, A074664, A095993.
Sequence in context: A085615 A054726 A003576 * A177388 A124453 A000165
Adjacent sequences: A095986 A095987 A095988 * A095990 A095991 A095992
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KEYWORD
| nonn
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AUTHOR
| Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Jul 18 2004
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