A346317 Number of permutations of [n] having two 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, 3, 11, 40, 148, 560, 2160, 8448, 33344, 132352, 527104, 2103296, 8401920, 33583104, 134279168, 537001984, 2147762176, 8590524416, 34360983552, 137441574912, 549761318912, 2199034789888, 8796117139456, 35184422420480, 140737593212928, 562950171525120

Offset: 2

Author

Alois P. Heinz, Jul 13 2021

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-20,16).

Crossrefs

Column k=2 of A344855.

Formula

G.f.: (4*x^3-7*x^2+5*x-1)*x^2/((4*x-1)*(2*x-1)^2).

For n>2, a(n) = 2^(2*n-5) + (n-1)*2^(n-4). - Vaclav Kotesovec, Jul 15 2021