|
| |
|
|
A276723
|
|
Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most seven elements.
|
|
6
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
|
|
|
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).
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
