A293850 Number of set partitions of [n^2] that are invariant under a permutation consisting of n n-cycles.

1, 1, 7, 42, 931, 6078, 560124, 3451290, 504673027, 10212362573, 1083069266634, 17595339114554, 13211434169884204, 109469680507411214, 36642712015230282784, 3131089417758323092388, 735014776353108421594259, 19549131844625243949179686

Offset: 0

Author

Alois P. Heinz, Oct 17 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..281

Crossrefs

Cf. A162663.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(binomial(n-1, j-1)
       *add(d^(j-1), d=numtheory[divisors](k))*b(n-j, k), j=1..n))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..18);

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[Binomial[n - 1, j - 1] Sum[d^(j - 1), {d, Divisors[k]}] b[n - j, k], {j, 1, n}]];
a[n_] := b[n, n];
a /@ Range[0, 18] (* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)

Formula

a(n) = A162663(n,n).