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A332856
Number of entries in the seventh cycles of all permutations of [n] when cycles are ordered by decreasing lengths.
2
1, 29, 583, 10366, 177299, 3029643, 52724894, 944353801, 17510885251, 337239557401, 6756438503137, 140893616636126, 3057901614671778, 69040616816923804, 1620394508763080044, 39500148841295346478, 999160362731046844470, 26200784568622019301658
OFFSET
7,2
LINKS
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, 7)[2]:
seq(a(n), n=7..24);
CROSSREFS
Column k=7 of A322384.
Sequence in context: A020766 A069295 A103723 * A287050 A142521 A032630
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 26 2020
STATUS
approved