A321282 Number of set partitions of [n^2] into n subsets having the same sum.

1, 1, 1, 9, 2650, 100664383, 808087012923418

Offset

0,4

Links

Table of n, a(n) for n=0..6.

Wikipedia, Partition of a set

Formula

a(n) = A275714(n^2,n).

Example

a(3) = 9: 12345|69|78, 1239|456|78, 1248|357|69, 1257|348|69, 1347|258|69, 1356|249|78, 159|2346|78, 168|249|357, 159|267|348.

Maple

b:= proc(l, n) option remember; `if`(n=0, 1, add(`if`(n>l[j],
       0, b(sort(subsop(j=l[j]-n, l)), n-1)), j=1..nops(l)))
    end:
a:= n-> b([n*(1+n^2)/2$n], n^2)/n!:
seq(a(n), n=0..5);

Mathematica

b[l_, n_] := b[l, n] = If[n == 0, 1, Sum[If[n > l[[j]], 0, b[Sort[ ReplacePart[l, j -> l[[j]] - n]], n-1]], {j, 1, Length[l]}]];
a[n_] := b[Table[n(1+n^2)/2, {n}], n^2]/n!;
a /@ Range[0, 5] (* Jean-François Alcover, May 04 2020, after Maple *)

Crossrefs

Cf. A007785, A275714, A317807, A321230.

Sequence in context: A069704 A033997 A068729 * A159775 A281538 A335010

Adjacent sequences: A321279 A321280 A321281 * A321283 A321284 A321285

Keyword

nonn,more

Author

Alois P. Heinz, Nov 01 2018

Status

approved