A219275 Number of standard Young tableaux for partitions of nonnegative integers into distinct parts with largest part n.

1, 1, 3, 25, 1069, 368168, 1299366501, 55208013380403, 32401197537296758130, 297072961835477978342245712, 47538199827835784548062928051198402, 146779873623344672821145371965795071455181183, 9581411392319396646028223743176779937161862866453789852

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

Column sums of A219274.

First differences of A219273.

Sequence in context: A350902 A306792 A012764 * A101733 A309116 A094815

Adjacent sequences: A219272 A219273 A219274 * A219276 A219277 A219278

Keyword

nonn

Author

Alois P. Heinz, Nov 17 2012

Status

approved