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A093789 Hook products of all partitions of 10. 0


%S 4725,6400,6400,6912,6912,8064,8064,8100,10368,10368,11520,11520,

%T 12096,12096,12600,12600,14400,14400,16128,16128,17280,17280,22680,

%U 22680,28800,28800,40320,40320,43200,43200,48384,48384,86400,86400,100800,100800,103680,103680,403200,403200,3628800,3628800

%N Hook products of all partitions of 10.

%C a(n)=10!/A003874(n). All 42 terms of this finite sequence are shown.

%p 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(10)[q])),q=1..numbpart(10))]);

%Y Cf. A003874.

%K fini,full,nonn

%O 1,1

%A _Emeric Deutsch_, May 17 2004

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)