A093792 Hook products of all partitions of 13.

290304, 290304, 302400, 302400, 362880, 362880, 388800, 414720, 414720, 483840, 483840, 518400, 518400, 518400, 518400, 537600, 537600, 544320, 544320, 604800, 604800, 665280, 665280, 691200, 691200, 725760, 725760, 725760, 798336, 798336, 844800, 844800, 907200

Offset

1,1

Links

Jean-François Alcover, Table of n, a(n) for n = 1..101

Formula

a(n) = 13!/A003877(102-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(13)[q])), q=1..numbpart(13))]);

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[13!/T[13]] (* Jean-François Alcover, Sep 22 2024, after Alois P. Heinz in A060240 *)

Crossrefs

Cf. A003877, A060240.

Row n=13 of A093784.

Sequence in context: A237147 A237556 A121742 * A068241 A250618 A252992

Adjacent sequences: A093789 A093790 A093791 * A093793 A093794 A093795

Keyword

fini,full,nonn

Author

Emeric Deutsch, May 17 2004

Status

approved