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A093787
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Hook products of all partitions of 9.
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0
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1680, 1680, 1920, 1920, 2160, 2160, 2240, 2240, 3024, 3024, 3456, 3456, 4320, 4320, 5184, 6480, 6480, 7560, 7560, 8640, 8640, 8640, 12960, 12960, 13440, 13440, 45360, 45360, 362880, 362880
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OFFSET
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1,1
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COMMENTS
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LINKS
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MAPLE
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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(9)[q])), q=1..numbpart(9))]);
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MATHEMATICA
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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, {}];
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CROSSREFS
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KEYWORD
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fini,full,nonn,changed
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AUTHOR
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STATUS
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approved
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