A276721 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most five elements.

1, 1, 2, 5, 15, 52, 151, 409, 1100, 3012, 8487, 23949, 67179, 187431, 521889, 1455667, 4066220, 11363476, 31747666, 88659265, 247559056, 691294366, 1930595096, 5391864630, 15058449487, 42054270461, 117445036871, 327989716409, 915985822220, 2558107420307

Offset: 0

Author

Alois P. Heinz, Sep 16 2016

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Wikipedia, Partition of a set

Crossrefs

Column k=5 of A276719.

Cf. A276839, A276895.

Formula

G.f.: -(x^8 +x^6 +3*x^5 +2*x^3 +x^2 -1)/((x+1) *(x^15 +3*x^14 -x^13 +5*x^12 +15*x^11 +14*x^10 +9*x^9 +13*x^8 -17*x^7 -7*x^6 -21*x^5 -3*x^3 -2*x +1)).