|
Search: id:A160181
|
|
|
| A160181 |
|
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. |
|
+0
1
|
|
| 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; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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.
|
|
FORMULA
|
See formulae for A000296.
|
|
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.
|
|
CROSSREFS
|
Cf. A000296, A005001, A000110.
Sequence in context: A005248 A032102 A100388 this_sequence A143874 A073641 A117763
Adjacent sequences: A160178 A160179 A160180 this_sequence A160182 A160183 A160184
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Anonymous, May 03 2009
|
|
|
Search completed in 0.002 seconds
|
