A250119 Triangle read by rows: T(n,m) (n >= 1, 1 <= m <= n) = number of set partitions of [n], avoiding 123454, with m blocks.

1, 1, 1, 1, 3, 1, 1, 7, 6, 1, 1, 15, 25, 10, 1, 1, 31, 90, 65, 14, 1, 1, 63, 301, 350, 121, 18, 1, 1, 127, 966, 1701, 834, 193, 22, 1, 1, 255, 3025, 7770, 5037, 1606, 281, 26, 1, 1, 511, 9330, 34105, 27918, 11461, 2730, 385, 30, 1, 1, 1023, 28501, 145750, 145777, 73762, 22381, 4270, 505, 34, 1

Offset

1,5

Links

Lars Blomberg, Table of n, a(n) for n = 1..5050 (The first 100 rows.)

Harry Crane, Left-right arrangements, set partitions, and pattern avoidance, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.

Example

Triangle begins:
  1;
  1,    1;
  1,    3,     1;
  1,    7,     6,      1;
  1,   15,    25,     10,      1;
  1,   31,    90,     65,     14,     1;
  1,   63,   301,    350,    121,    18,     1;
  1,  127,   966,   1701,    834,   193,    22,    1;
  1,  255,  3025,   7770,   5037,  1606,   281,   26,   1;
  1,  511,  9330,  34105,  27918, 11461,  2730,  385,  30,  1;
  1, 1023, 28501, 145750, 145777, 73762, 22381, 4270, 505, 34, 1;
  ...

Crossrefs

Cf. A112857, A250118. A163942 is a diagonal.

Sequence in context: A202181 A130749 A250118 * A154959 A080417 A008277

Adjacent sequences: A250116 A250117 A250118 * A250120 A250121 A250122

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 25 2014

Extensions

a(46)-a(66) from Lars Blomberg, Aug 17 2017

Status

approved