A093790 Hook products of all partitions of 11.

17280, 17280, 25920, 25920, 30240, 30240, 32400, 32400, 33600, 34560, 34560, 36288, 36288, 40320, 40320, 40320, 40320, 43200, 43200, 48384, 48384, 57600, 57600, 60480, 60480, 67200, 67200, 72576, 72576, 86400, 86400, 103680, 103680, 120960, 120960, 158400, 172800, 172800, 190080, 190080, 241920, 241920, 302400, 302400, 332640, 332640, 362880, 362880, 887040, 887040, 907200, 907200, 3991680, 3991680, 39916800, 39916800

Offset: 1

Author

Emeric Deutsch, May 17 2004

Keywords

• fini
• full
• nonn

Comments

All 56 terms of this finite sequence are shown.

Crossrefs

Cf. A003875, A060240.

Row n=11 of A093784.

Programs

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(11)[q])), q=1..numbpart(11))]);

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[11!/T[11]] (* Jean-François Alcover, Sep 05 2024, after Alois P. Heinz in A060240 *)

Formula

a(n) = 11!/A003875(57-n).