OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..22
Wikipedia, Young tableau
EXAMPLE
a(2) = 3:
+------+ +------+ +------+
| 1 2 | | 1 3 | | 1 2 |
| 3 .--+ | 2 .--+ +------+
+---+ +---+
MAPLE
h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+
add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
end:
b:= (n, l)-> `if`(n<1, h(l), b(n-1, l) +b(n-1, [l[], n])):
a:= n-> `if`(n=0, 1, b(n-1, [n])):
seq(a(n), n=0..12);
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}]];
b[n_, l_] := If[n < 1, h[l], b[n - 1, l] + b[n - 1, Append[l, n]]];
a[n_] := If[n == 0, 1, b[n - 1, {n}]];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Nov 02 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 17 2012
STATUS
approved