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

0,3

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).

Crossrefs

Column k=6 of A276837.

Cf. A276722.

Sequence in context: A263750 A263751 A263745 * A364426 A178011 A189853

Adjacent sequences: A276837 A276838 A276839 * A276841 A276842 A276843

Keyword

nonn,easy

Author

Alois P. Heinz, Sep 20 2016

Status

approved