A276722 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most six elements.

1, 1, 2, 5, 15, 52, 203, 674, 2066, 6184, 18587, 56867, 178317, 561319, 1760125, 5489888, 17057701, 52931331, 164466672, 511758485, 1593612234, 4962950389, 15451453190, 48088784307, 149640967002, 465653853729, 1449146745582, 4510183339086, 14037494547193

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=6 of A276719.

Cf. A276840, A276896.

Formula

G.f.: -(x^22 -x^19 -15*x^18 +7*x^17 +18*x^16 +11*x^14 -22*x^13 -26*x^12 -10*x^11 +2*x^10 -28*x^9 +3*x^8 +16*x^7 +14*x^6 -5*x^5 +5*x^4 +5*x^3 +2*x^2 -1) / (x^32 +5*x^31 +x^30 -5*x^29 -6*x^28 -111*x^27 -210*x^26 +52*x^25 +263*x^24 +85*x^23 -346*x^22 -882*x^21 -401*x^20 +584*x^19 +382*x^18 -1058*x^17 -1319*x^16 -200*x^15 +250*x^14 +382*x^13 +589*x^12 +716*x^11 +346*x^10 +49*x^9 -137*x^8 -146*x^7 -84*x^6 -3*x^5 -4*x^4 -5*x^3 -3*x^2 -x +1).