A346319 Number of permutations of [n] having four 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, 10, 85, 665, 5033, 37632, 280760, 2100560, 15799344, 119598336, 911432704, 6991479040, 53960703232, 418803056640, 3266623490048, 25590201536512, 201220024528896, 1587256170708992, 12553933544030208, 99511621823561728, 790240133265817600, 6284788112052715520

Offset: 4

Author

Alois P. Heinz, Jul 13 2021

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000
• Index entries for linear recurrences with constant coefficients, signature (40,-700,7056,-45360,194304,-561728,1082624,-1332224,946176,-294912).

Crossrefs

Column k=4 of A344855.

Formula

G.f.: (18432*x^10 -68352*x^9 +115136*x^8 -117072*x^7 +80628*x^6 -38652*x^5 +12733*x^4 -2791*x^3 +385*x^2 -30*x+1)*x^4 / ((8*x-1) *(6*x-1)^2 *(4*x-1)^3 *(2*x-1)^4).