A093769 Hook products of all partitions of 7.

144, 144, 240, 240, 252, 336, 336, 360, 360, 360, 360, 840, 840, 5040, 5040

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Formula

a(n) = 7!/A003871(16-n).

Maple

H:=proc(pa) local F, j, p, Q, i, col, a, A: F:=proc(x) local i, ct: ct:=0: for i from 1 to nops(x) do if x[i]>1 then ct:=ct+1 else fi od: ct; end: for j from 1 to nops(pa) do p[1][j]:=pa[j] od: Q[1]:=[seq(p[1][j], j=1..nops(pa))]: for i from 2 to pa[1] do for j from 1 to F(Q[i-1]) do p[i][j]:=Q[i-1][j]-1 od: Q[i]:=[seq(p[i][j], j=1..F(Q[i-1]))] od: for i from 1 to pa[1] do col[i]:=[seq(Q[i][j]+nops(Q[i])-j, j=1..nops(Q[i]))] od: a:=proc(i, j) if i<=nops(Q[j]) and j<=pa[1] then Q[j][i]+nops(Q[j])-i else 1 fi end: A:=matrix(nops(pa), pa[1], a): product(product(A[m, n], n=1..pa[1]), m=1..nops(pa)); end: with(combinat): rev:=proc(a) [seq(a[nops(a)+1-i], i=1..nops(a))] end: sort([seq(H(rev(partition(7)[q])), q=1..numbpart(7))]);

Mathematica

h[l_] := With[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j, 1, l[[i]]}], {i, 1, n}]];
g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Array[1&, n]]], If[i < 1, 0, Flatten@Table[g[n - i*j, i - 1, Join[l, Array[i&, j]]], {j, 0, n/i}]]];
T[n_] := g[n, n, {}];
Sort[7!/T[7]] (* Jean-François Alcover, Aug 12 2024, after Alois P. Heinz in A060240 *)

Crossrefs

Row n=7 of A093784.

Cf. A003871, A060240.

Sequence in context: A350453 A374988 A056628 * A124512 A199546 A101936

Adjacent sequences: A093766 A093767 A093768 * A093770 A093771 A093772

Keyword

fini,full,nonn

Author

Emeric Deutsch, May 17 2004

Status

approved