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A093786 Hook products of all partitions of 8. 0
448, 576, 576, 630, 630, 720, 720, 960, 1152, 1152, 1440, 1440, 1920, 1920, 2016, 2016, 2880, 2880, 5760, 5760, 40320, 40320 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..22.

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

CROSSREFS

Cf. A003872.

Sequence in context: A147628 A153486 A062040 * A251646 A235177 A346514

Adjacent sequences:  A093783 A093784 A093785 * A093787 A093788 A093789

KEYWORD

fini,full,nonn

AUTHOR

Emeric Deutsch, May 17 2004

STATUS

approved

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Last modified December 2 08:31 EST 2021. Contains 349437 sequences. (Running on oeis4.)