A215266 Number of solid standard Young tableaux of cylindrical shape lambda X 2, where lambda ranges over all partitions of n.

1, 1, 4, 26, 258, 3346, 54108, 1054256, 24161966, 634230122, 18806776982, 622011916184, 22754818956246, 912075762692584, 39755634279964662, 1872279469323840472, 94783193260373606758, 5135585509536795416348, 296656123838796109849526, 18200829821539972354967252

Offset: 0

Author

Alois P. Heinz, Aug 07 2012

Keywords

• nonn

Links

• S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012
• Wikipedia, Young tableau

Crossrefs

Column k=2 of A215204.

Programs

Maple

b:= proc(l) option remember; local m; m:= nops(l);
      `if`({map(x-> x[], l)[]}minus{0}={}, 1, add(add(`if`(l[i][j]>
      `if`(i=m or nops(l[i+1])
      `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:
g:= proc(n, i, l) `if`(n=0 or i=1, b(map(x->[2$x], [l[], 1$n])),
       add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))
    end:
a:= n-> g(n, n, []):
seq(a(n), n=0..12);