A276722 - OEIS

%I #8 Sep 22 2016 08:06:44

%S 1,1,2,5,15,52,203,674,2066,6184,18587,56867,178317,561319,1760125,

%T 5489888,17057701,52931331,164466672,511758485,1593612234,4962950389,

%U 15451453190,48088784307,149640967002,465653853729,1449146745582,4510183339086,14037494547193

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

%H Alois P. Heinz, <a href="/A276722/b276722.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F 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).

%Y Column k=6 of A276719.

%Y Cf. A276840, A276896.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Sep 16 2016