A270954 Number of set partitions of [n] having no pairs (m,m+1) such that m+1 is in some block b and m is in block b+1.

1, 1, 2, 4, 9, 25, 84, 323, 1377, 6412, 32312, 174941, 1011357, 6210298, 40323011, 275763910, 1979709852, 14875239212, 116679269248, 953201694216, 8093501305721, 71291395351760, 650357174742217, 6134966541625355, 59759476024690454, 600309156303711764

Offset: 0

Author

Alois P. Heinz, Mar 26 2016

Keywords

• nonn

Examples

			a(3) = 4: 123, 12|3, 1|23, 1|2|3.
a(4) = 9: 1234, 123|4, 12|34, 12|3|4, 1|234, 1|23|4, 14|2|3, 1|2|34, 1|2|3|4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300
• Wikipedia, Partition of a set

Crossrefs

Column k=0 of A270953.

Programs

Maple

b:= proc(n, i, m) option remember; `if`(n=0, 1, add(
     `if`(j=i-1, 0, b(n-1, j, max(m, j))), j=1..m+1))
    end:
a:= n-> b(n, 1, 0):
seq(a(n), n=0..25);

Mathematica

b[n_, i_, m_] := b[n, i, m] = If[n == 0, 1, Sum[If[j == i - 1, 0, b[n - 1, j, Max[m, j]]], {j, 1, m + 1}]];
a[n_] := b[n, 1, 0];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 27 2018, translated from Maple *)