A151882 Let g be a permutation of [1..n] having say j_i cycles of length i, with Sum_i i*j_i = n; sequence gives Sum_g Sum_i (j_i)^2.

1, 5, 17, 80, 424, 2744, 19928, 166984, 1543176, 15939792, 178966512, 2200820544, 29089668672, 415261531008, 6316101256320, 102692213061120, 1766690411927040, 32235156493470720, 618870347081671680, 12523381062124032000, 265423904312781312000

Offset

1,2

Links

N. J. A. Sloane and Alois P. Heinz, Table of n, a(n) for n = 1..450 (first 30 terms from N. J. A. Sloane)

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add(multinomial(n, n-i*j, i$j)/j!*(i-1)!^j*(p-> p+
      [0, p[1]*j^2])(b(n-i*j, i-1)), j=0..n/i)))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..30);  # Alois P. Heinz, Oct 21 2015

Mathematica

multinomial[n_, k_] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n==0, {1, 0}, If[i<1, {0, 0}, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]] ]/j! * (i-1)!^j*Function[p, p+{0, p[[1]]*j^2}][b[n-i*j, i-1]], {j, 0, n/i}] ] ]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Mar 10 2017, after Alois P. Heinz *)

Crossrefs

Cf. A000254, A151881, A151883.

Sequence in context: A307052 A369262 A053418 * A359206 A149749 A149750

Adjacent sequences: A151879 A151880 A151881 * A151883 A151884 A151885

Keyword

nonn

Author

N. J. A. Sloane, Jul 22 2009

Status

approved