|
|
A321282
|
|
Number of set partitions of [n^2] into n subsets having the same sum.
|
|
2
|
|
|
|
OFFSET
|
0,4
|
|
LINKS
|
|
|
FORMULA
|
|
|
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!;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|