A276841 Number of permutations of [n] such that for each cycle c the smallest integer interval containing all elements of c has at most seven elements.
1, 1, 2, 6, 24, 120, 720, 5040, 20160, 75600, 287280, 1133550, 4686660, 20368569, 93109737, 406088940, 1719126780, 7184340564, 29966843736, 125593803792, 530881463680, 2267064321984, 9681953067016, 41200660295772, 174712473986620, 739333708856220
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Formula
G.f.: -(x^52 +6*x^50 -34*x^49 +20*x^48 +482*x^47 -426*x^46 -1468*x^45 -4536*x^44 +3648*x^43 +19218*x^42 +980*x^41 +11510*x^40 -47116*x^39 +35786*x^38 +93064*x^37 +164632*x^36 +300102*x^35 -85560*x^34 -604736*x^33 +93922*x^32 -445966*x^31 +372558*x^30 +156416*x^29 +160198*x^28 -518168*x^27 -147664*x^26 -493240*x^25 +29594*x^24 +313562*x^23 +610220*x^22 +32062*x^21 -12854*x^20 +13220*x^19 -157960*x^18 -46776*x^17 -70050*x^16 -41076*x^15 -50710*x^14 -5996*x^13 +1894*x^12 -1936*x^11 +968*x^10 +738*x^9 +1040*x^8 +776*x^7 -2*x^6 +70*x^5 +34*x^4 +8*x^3 +2*x^2 -1) / (x^64 +11*x^63 +15*x^62 -31*x^61 +21*x^60 -881*x^59 +6397*x^58 +41653*x^57 +32901*x^56 -67903*x^55 -284725*x^54 -392391*x^53 +559947*x^52 +104334*x^51 -1200042*x^50 -2062678*x^49 -1572286*x^48 +15473434*x^47 +15863554*x^46 +35936394*x^45 +69616662*x^44 -80992842*x^43 -307844474*x^42 -283307502*x^41 -219491322*x^40 +338286*x^39 +213380440*x^38 -3315412*x^37 -349666888*x^36 -484336364*x^35 -431418124*x^34 -248674504*x^33 +22949740*x^32 +144629920*x^31 -9726680*x^30 -113690432*x^29 -126317520*x^28 -143609200*x^27 -79336148*x^26 +10701066*x^25 -42072302*x^24 -78959890*x^23 -72447322*x^22 -22061410*x^21 -5812154*x^20 -8720370*x^19 -2145534*x^18 +2011058*x^17 +2823538*x^16 +1655238*x^15 +661954*x^14 +294538*x^13 +118975*x^12 +23793*x^11 -13327*x^10 -11405*x^9 -7057*x^8 -3807*x^7 -305*x^6 -93*x^5 -37*x^4 -9*x^3 -3*x^2 -x +1).