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A196236 Number of different ways to select 9 disjoint subsets from {1..n} with equal element sum.

%I A196236 #18 Sep 02 2019 14:40:10
%S A196236 1,3,14,40,156,554,2369,11841,60654,498320,2987689,15177178,96041346,
%T A196236 656938806,4640699138,31263742313,221075005249
%N A196236 Number of different ways to select 9 disjoint subsets from {1..n} with equal element sum.
%e A196236 a(18) = 3: {1,16}, {2,15}, {3,14}, {4,13}, {5,12}, {6,11}, {7,10}, {8,9}, {17} have element sum 17; {1,17}, {2,16}, {3,15}, {4,14}, {5,13}, {6,12}, {7,11}, {8,10}, {18} have element sum 18; {1,18}, {2,17}, {3,16}, {4,15}, {5,14}, {6,13}, {7,12}, {8,11}, {9,10} have element sum 19.
%t A196236 b[l_, n_, k_] := b[l, n, k] = Module[{i, j}, If[l == Array[0 &, k], 1, If[Total[l] > n*(n - 1)/2, 0, b[l, n - 1, k]] + Sum[If[l[[j]] - n < 0, 0, b[Sort[Table[l[[i]] - If[i == j, n, 0], {i, 1, k}]], n - 1, k]], {j, 1, k}]]];
%t A196236 T[n_, k_] := Sum[b[Array[t &, k], n, k], {t, 2*k - 1, Floor[n*(n+1)/(2*k) ]}]/k!;
%t A196236 a[n_] := T[n, 9];
%t A196236 Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 17, 25}] (* _Jean-François Alcover_, Jun 08 2018, after _Alois P. Heinz_ *)
%Y A196236 Column k=9 of A196231. Cf. A000225, A161943, A164934, A164949, A196232, A196233, A196234, A196235, A196237.
%K A196236 nonn,more
%O A196236 17,2
%A A196236 _Alois P. Heinz_, Sep 29 2011
%E A196236 a(29) from _Alois P. Heinz_, Nov 05 2014
%E A196236 a(30)-a(33) from _Bert Dobbelaere_, Sep 02 2019