A276723 Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most seven elements.
1, 1, 2, 5, 15, 52, 203, 877, 3263, 11155, 36810, 120635, 398736, 1340561, 4605989, 15908448, 54826671, 188085307, 642431001, 2188102307, 7446095610, 25366540627, 86531467800, 295449388797, 1009134603216, 3446558809107, 11767813404774, 40167156826109
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Pierpaolo Natalini, Paolo Emilio Ricci, New Bell-Sheffer Polynomial Sets, Axioms 2018, 7(4), 71.
- Wikipedia, Partition of a set
Formula
G.f.: -(x^52 +2*x^50 -9*x^49 +5*x^48 +93*x^47 -46*x^46 -18*x^45 -439*x^44 +166*x^43 +919*x^42 -369*x^41 +1431*x^40 -2154*x^39 +1497*x^38 +2366*x^37 +7382*x^36 +4861*x^35 +3348*x^34 -12721*x^33 +1916*x^32 -7481*x^31 +8799*x^30 +8061*x^29 +10105*x^28 -8760*x^27 +3274*x^26 -9925*x^25 -873*x^24 +8803*x^23 +13626*x^22 -2818*x^21 +2263*x^20 +3291*x^19 -5707*x^18 -3550*x^17 -4115*x^16 -2399*x^15 -2475*x^14 -877*x^13 +461*x^12 +130*x^11 +226*x^10 +182*x^9 +243*x^8 +161*x^7 -4*x^6 +21*x^5 +14*x^4 +5*x^3 +2*x^2 -1) / (x^64 +6*x^63 +3*x^62 -2*x^61 -24*x^60 +7*x^59 +981*x^58 +2410*x^57 +1066*x^56 -2882*x^55 -8931*x^54 -2882*x^53 -4007*x^52 -30225*x^51 -9863*x^50 +20863*x^49 +101214*x^48 +127153*x^47 +158805*x^46 +285147*x^45 +101665*x^44 -513829*x^43 -895778*x^42 -800589*x^41 -572933*x^40 +290605*x^39 +232843*x^38 -841969*x^37 -1610201*x^36 -1642130*x^35 -1731114*x^34 -642745*x^33 +245579*x^32 -62183*x^31 -769603*x^30 -803729*x^29 -905469*x^28 -727539*x^27 -323095*x^26 -229154*x^25 -442563*x^24 -447061*x^23 -251676*x^22 -41018*x^21 -74736*x^20 -74741*x^19 +35465*x^18 +81095*x^17 +72575*x^16 +39983*x^15 +23409*x^14 +14506*x^13 +3868*x^12 -628*x^11 -1927*x^10 -1426*x^9 -935*x^8 -468*x^7 -31*x^6 -20*x^5 -13*x^4 -5*x^3 -3*x^2 -x +1).