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A160181
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a(n) is the total number of partitions of sets containing from 0 to n elements into blocks of at least 2 elements. It is the sum of the first n+1 terms of A000296.
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1, 1, 2, 3, 7, 18, 59, 221, 936, 4361, 22083, 120336, 700653, 4333933, 28345090, 195233255, 1411303635, 10675375402, 84276173439, 692752181561, 5917018378496, 52416910416933, 480786834535250, 4559132648864259
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is the total number of complete rhyme schemes for 0 to n lines; in other words, a(n) is the total number of rhyme schemes for 0 to n lines where each line rhymes with at least one other line.
If the restriction that the blocks of the partitions must have at least 2 elements is removed, then A005001 is obtained except for the first term of A005001.
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FORMULA
| See formulae for A000296.
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EXAMPLE
| a(7)=221 because the total number of partitions of sets containing from 0 to 7 elements into blocks of at least 2 elements is 221. The first n+1=8 terms of A000296 are 1,0,1,1,4,11,41,162 and 1+0+1+1+4+11+41+162=221.
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CROSSREFS
| Cf. A000296, A005001, A000110.
Sequence in context: A032102 A100388 A186232 * A143874 A073641 A117763
Adjacent sequences: A160178 A160179 A160180 * A160182 A160183 A160184
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KEYWORD
| easy,nonn
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AUTHOR
| Anonymous, May 03 2009
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