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A093786 Hook products of all partitions of 8. 0

%I #2 Mar 30 2012 17:35:55

%S 448,576,576,630,630,720,720,960,1152,1152,1440,1440,1920,1920,2016,

%T 2016,2880,2880,5760,5760,40320,40320

%N Hook products of all partitions of 8.

%C a(n)=8!/A003872(n)

%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(8)[q])),q=1..numbpart(8))]);

%Y Cf. A003872.

%K fini,full,nonn

%O 1,1

%A _Emeric Deutsch_, May 17 2004

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)