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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Partition of a set

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).

Crossrefs

Column k=6 of A276719.

Cf. A276840, A276896.

Sequence in context: A306551 A110038 A343666 * A287584 A287277 A287255

Adjacent sequences: A276719 A276720 A276721 * A276723 A276724 A276725

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 16 2016

Status

approved