A346323 Number of permutations of [n] having eight 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, 36, 870, 17490, 317031, 5390814, 87942569, 1395590625, 21740278417, 334497665216, 5105159585136, 77525496199008, 1173978347855008, 17756444087253504, 268561449630791680, 4065329910324860672, 61628507048573158144, 936035967482288414720

Offset: 8

Author

Alois P. Heinz, Jul 13 2021

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..838
• Index entries for linear recurrences with constant coefficients, signature (240, -27720, 2052512, -109501392, 4485157248, -146762730752, 3941544701952, -88583039660544, 1690201339101184, -27683252247785472, 392554888743665664, -4851695318748831744, 52537637204482129920, -500491057082699612160, 4207381516172517703680, -31281978226696900116480, 206014309171875372072960, -1202762064346113966080000, 6226143028325392507207680, -28563943556332339917225984, 116011182450800820653916160, -416382609918980503445176320, 1317358503859988420213342208, -3661679575789298214196215808, 8903229523611559893896527872, -18833310289690908029676945408, 34420123100871095086594654208, -53876192282750532975146827776, 71417640290027267167749144576, -79011046920360642901671149568, 71540341196238752070915588096, -51594033438349863071458000896, 28478927494742679928795299840, -11290083667294698757265817600, 2859932711332506431913984000, -347485857744891213250560000).

Crossrefs

Column k=8 of A344855.

Programs

Maple

b:= proc(n) option remember; series(`if`(n=0, 1, add(b(n-j)
      *binomial(n-1, j-1)*x*ceil(2^(j-2)), j=1..n)), x, 9)
    end:
a:= n-> coeff(b(n), x, 8):
seq(a(n), n=8..29);