|
Search: id:A056858
|
|
|
| A056858 |
|
Triangle of number of rises in set partitions of n. |
|
+0
2
|
|
| 1, 1, 1, 1, 3, 1, 1, 6, 7, 1, 1, 10, 26, 14, 1, 1, 15, 71, 89, 26, 1, 1, 21, 161, 380, 267, 46, 1, 1, 28, 322, 1268, 1709, 732, 79, 1, 1, 36, 588, 3571, 8136, 6794, 1887, 133, 1, 1, 45, 1002, 8878, 31532, 44924, 24717, 4654, 221, 1, 1, 55, 1617, 20053, 104927, 234412
(list; table; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
Number of rises s_{i+1} > s_i in a set partition {s_1, ..., s_n} of {1, ..., n}, where s_i is the subset containing i, s(1) = 1, and s(i) <= 1 + max of previous s(j)'s.
|
|
REFERENCES
|
W. C. Yang, Conjectures on some sequences involving set partitions and Bell numbers, preprint, 2000.
|
|
EXAMPLE
|
For example {1, 2, 1, 2, 2, 3} is a set partition of {1, 2, 3, 4, 5, 6} and has 3 rises, at i = 1, i = 3, and i = 5.
1; 1,1; 1,3,1; 1,6,7,1; 1,10,26,14,1; 1,15,71,89,26,1; ...
|
|
CROSSREFS
|
Cf. Bell numbers A000110.
Cf. A056857-A056863.
Column 1 is triangular numbers (A000217); diagonal T(n, n-1) appears to be A001924.
Sequence in context: A131235 A133713 A008278 this_sequence A137251 A046716 A123354
Adjacent sequences: A056855 A056856 A056857 this_sequence A056859 A056860 A056861
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Winston C. Yang (winston(AT)cs.wisc.edu), Aug 31 2000
|
|
EXTENSIONS
|
More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 08 2006
|
|
|
Search completed in 0.002 seconds
|
