A346320 Number of permutations of [n] having five 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, 15, 175, 1820, 17913, 171465, 1619090, 15203100, 142623624, 1340443104, 12641487040, 119734858880, 1139445627392, 10895927375616, 104687442226688, 1010398777492480, 9793403768723456, 95295673342836736, 930591031216799744, 9116681462478864384

Offset: 5

Author

Alois P. Heinz, Jul 13 2021

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (70, -2240, 43456, -571424, 5393344, -37736448, 199267328, -800498944, 2446126592, -5639102464, 9631809536, -11801133056, 9794617344, -4926210048, 1132462080).

Crossrefs

Column k=5 of A344855.

Formula

G.f.: (35389440*x^15 -171638784*x^14 [phone]*x^13 -541806592*x^12 [phone]*x^11 -379603968*x^10 [phone]*x^9 -89384640*x^8 [phone]*x^7 -7487228*x^6 +1432429*x^5 -202097*x^4 +20286*x^3 -1365*x^2 +55*x -1)*x^5 / ((10*x-1) *(8*x-1)^2 *(6*x-1)^3 *(4*x-1)^4 *(2*x-1)^5).