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A321282 Number of set partitions of [n^2] into n subsets having the same sum. 2
1, 1, 1, 9, 2650, 100664383, 808087012923418 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 9 18:32 EDT 2020. Contains 336326 sequences. (Running on oeis4.)