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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.
2
1, 6, 35, 195, 1078, 5992, 33632, 190800, 1093664, 6327552, 36904192, 216676096, 1279012352, 7581628416, 45086720000, 268774576128, 1605129183232, 9598558142464, 57453899350016, 344139257020416, 2062361588793344, 12363724057214976, 74138363625472000
OFFSET
3,2
LINKS
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
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 *)
CROSSREFS
Column k=3 of A344855.
Sequence in context: A254826 A274373 A328331 * A009572 A027202 A026934
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jul 13 2021
STATUS
approved