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A276841
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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.
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3
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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
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OFFSET
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0,3
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LINKS
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FORMULA
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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).
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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