A346322 Number of permutations of [n] having seven 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, 28, 546, 9030, 136521, 1956570, 27124955, 368258891, 4934711782, 65608599056, 868543125632, 11476719098208, 151628071536832, 2005351952310016, 26570735233245952, 352902891363604736, 4699994984738296320, 62779734338836996096, 841132871051793858560

Offset: 7

Author

Alois P. Heinz, Jul 13 2021

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..879
• Index entries for linear recurrences with constant coefficients, signature (168, -13440, 681632, -24615360, 673960320, -14545867776, 254017792512, -3655881782784, 43944394303488, -445483185094656, 3835837793820672, -28195256256282624, 177510573498728448, -958975703677403136, 4447744859322580992, -17695513525640822784, 60260448721418846208, -175010175041662877696, 431158568263920648192, -894423403170908602368, 1546792199062741319680, -2199976821097607725056, 2525948081813952921600, -2280501363206944456704, 1556924686713055346688, -754785240817587978240, 231325591660815974400, -33664847019245568000).

Crossrefs

Column k=7 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, 8)
    end:
a:= n-> coeff(b(n), x, 7):
seq(a(n), n=7..29);