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

8,2

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

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);

Crossrefs

Column k=8 of A322384.

Sequence in context: A159174 A219125 A103724 * A237857 A306472 A014935

Adjacent sequences: A332854 A332855 A332856 * A332858 A332859 A332860

Keyword

nonn

Author

Alois P. Heinz, Feb 26 2020

Status

approved