login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A332854 Number of entries in the fifth cycles of all permutations of [n] when cycles are ordered by decreasing lengths. 2
1, 16, 197, 2311, 27568, 343909, 4541329, 63719723, 949770615, 15010838233, 250997692441, 4430433962701, 82376202579421, 1610014961936672, 33010385435710028, 708642421376230354, 15899009565671538930, 372166745683645768206, 9074749796104015627262 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..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, 5)[2]:

seq(a(n), n=5..23);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

b[n_, i_, t_] := b[n, i, t] = If[n == 0, {1, 0}, If[i<1, {0, 0},

     Sum[Function[p, p + If[t > 0 && t - j < 1, {0, p[[1]]*i},

     {0, 0}]][(i-1)!^j*b[n - i*j, Min[n - i*j, i-1], Max[0, t-j]]/j!*

     multinomial[n, Append[Table[i, {j}], n - i*j]]], {j, 0, n/i}]]];

a[n_] := b[n, n, 5][[2]];

Table[a[n], {n, 5, 23}] (* Jean-Fran├žois Alcover, Mar 13 2021, after Alois P. Heinz *)

CROSSREFS

Column k=5 of A322384.

Sequence in context: A093060 A153885 A016226 * A154240 A081679 A154249

Adjacent sequences:  A332851 A332852 A332853 * A332855 A332856 A332857

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 26 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 20:09 EDT 2021. Contains 348044 sequences. (Running on oeis4.)