|
| |
|
|
A214631
|
|
Number A(n,k) of solid standard Young tableaux of shape [[(n)^(k+1)],[n]^k]; square array A(n,k), n>=0, k>=0, read by antidiagonals.
|
|
3
|
|
|
|
1, 1, 1, 1, 2, 1, 1, 6, 16, 1, 1, 20, 936, 192, 1, 1, 70, 85800, 379366, 2816, 1, 1, 252, 9962680, 1825221320, 249664758, 46592, 1, 1, 924, 1340103744, 14336196893200, 89261675900020, 221005209058, 835584, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,5
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
Square array A(n,k) begins:
1, 1, 1, 1, 1, ...
1, 2, 6, 20, 70, ...
1, 16, 936, 85800, 9962680, ...
1, 192, 379366, 1825221320, 14336196893200, ...
1, 2816, 249664758, 89261675900020, 70351928759681296000, ...
|
|
|
MAPLE
|
b:= proc(l) option remember; local m; m:= nops(l);
`if`({map(x-> x[], l)[]}={0}, 1, add(add(`if`(l[i][j]>
`if`(i=m or nops(l[i+1])<j, 0, l[i+1][j]) and l[i][j]>
`if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
end:
A:= (n, k)-> b([[n$(k+1)], [n]$k]):
seq(seq(A(n, d-n), n=0..d), d=0..8);
|
|
|
MATHEMATICA
|
b[l_] := b[l] = With[{m = Length[l]}, If[Union[Flatten[l]] == {0}, 1, Sum[Sum[If[l[[i, j]] > If[i == m || Length[l[[i+1]] ] < j, 0, l[[i+1, j]] ] && l[[i, j]] > If[Length[l[[i]] ] == j, 0, l[[i, j+1]] ], b[ReplacePart[l, i -> ReplacePart[l[[i]], j -> l[[i, j]]-1]]], 0], {j, 1, Length[l[[i]] ]}], {i, 1, m}]]]; a[n_, k_] := b[{Array[n&, k+1], Sequence @@ Array[{n}&, k]}]; Table[Table[a[n, d-n], {n, 0, d}], {d, 0, 8}] // Flatten (* Jean-François Alcover, Dec 18 2013, translated from Maple *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
