A276840 Number of permutations of [n] such that for each cycle c the smallest integer interval containing all elements of c has at most six elements.
1, 1, 2, 6, 24, 120, 720, 2520, 8400, 28728, 103050, 390555, 1566813, 5994636, 22318676, 82337580, 304360184, 1134352752, 4275368704, 16107425628, 60453074344, 226179710040, 845165016029, 3159696003981, 11832636916230, 44346582492034, 166184942954284
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Formula
G.f.: -(x^22 +2*x^20 -2*x^19 -44*x^18 +22*x^17 +60*x^16 -4*x^15 +40*x^14 -102*x^13 -120*x^12 -4*x^11 -8*x^10 -142*x^9 +2*x^8 +28*x^7 +42*x^6 -8*x^5 +12*x^4 +8*x^3 +2*x^2 -1) / (x^32 +9*x^31 +9*x^30 -19*x^29 +59*x^28 -461*x^27 -2227*x^26 -977*x^25 +2109*x^24 +655*x^23 -947*x^22 -8178*x^21 -13502*x^20 +1258*x^19 +11266*x^18 -12018*x^17 -32910*x^16 -12790*x^15 +2866*x^14 +6174*x^13 +4666*x^12 +5578*x^11 +3425*x^10 +1037*x^9 -523*x^8 -639*x^7 -449*x^6 -37*x^5 -15*x^4 -9*x^3 -3*x^2 -x +1).