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

%I A321282 #16 May 04 2020 21:31:03
%S A321282 1,1,1,9,2650,100664383,808087012923418
%N A321282 Number of set partitions of [n^2] into n subsets having the same sum.
%H A321282 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A321282 a(n) = A275714(n^2,n).
%e A321282 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.
%p A321282 b:= proc(l, n) option remember; `if`(n=0, 1, add(`if`(n>l[j],
%p A321282        0, b(sort(subsop(j=l[j]-n, l)), n-1)), j=1..nops(l)))
%p A321282     end:
%p A321282 a:= n-> b([n*(1+n^2)/2$n], n^2)/n!:
%p A321282 seq(a(n), n=0..5);
%t A321282 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]}]];
%t A321282 a[n_] := b[Table[n(1+n^2)/2, {n}], n^2]/n!;
%t A321282 a /@ Range[0, 5] (* _Jean-François Alcover_, May 04 2020, after Maple *)
%Y A321282 Cf. A007785, A275714, A317807, A321230.
%K A321282 nonn,more
%O A321282 0,4
%A A321282 _Alois P. Heinz_, Nov 01 2018