A332857 Number of entries in the eighth cycles of all permutations of [n] when cycles are ordered by decreasing lengths.

1, 37, 916, 19526, 392085, 7734663, 153275513, 3090075848, 63852563521, 1358480574137, 29837098126826, 677555150712614, 15919961048979164, 387124513859258764, 9741441909198136488, 253578333540120825224, 6825015749404715358362, 189819840262710177446426

Offset: 8

Author

Alois P. Heinz, Feb 26 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..450
• Andrew V. Sills, Integer Partitions Probability Distributions, arXiv:1912.05306 [math.CO], 2019.
• Wikipedia, Permutation

Crossrefs

Column k=8 of A322384.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))((i-1)!^j*
        b(n-i*j, min(n-i*j, i-1), max(0, t-j))/j!*
        combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
    end:
a:= n-> b(n$2, 8)[2]:
seq(a(n), n=8..26);