A346318 Number of permutations of [n] having three cycles of the form (c1, c2, ..., c_m) where c1 = min_{i>=1} c_i and c_j = min_{i>=j} c_i or c_j = max_{i>=j} c_i.

1, 6, 35, 195, 1078, 5992, 33632, 190800, 1093664, 6327552, 36904192, 216676096, 1279012352, 7581628416, 45086720000, 268774576128, 1605129183232, 9598558142464, 57453899350016, 344139257020416, 2062361588793344, 12363724057214976, 74138363625472000

Offset: 3

Author

Alois P. Heinz, Jul 13 2021

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (20,-160,656,-1456,1664,-768).

Crossrefs

Column k=3 of A344855.

Programs

Mathematica

Drop[CoefficientList[Series[(96x^6-256x^5+298x^4-201x^3+75x^2-14x+1)x^3/((6x-1)(4x-1)^2 (2x-1)^3),{x,0,30}],x],3] (* Harvey P. Dale, Jun 11 2024 *)

Formula

G.f.: (96*x^6-256*x^5+298*x^4-201*x^3+75*x^2-14*x+1)*x^3 / ((6*x-1) *(4*x-1)^2 *(2*x-1)^3).

For n>3, a(n) = 2^(n-7)*3^(n-1) + (n-2)*2^(2*n-8) + (n^2 - 3*n + 1)*2^(n-7). - Vaclav Kotesovec, Jul 15 2021