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%I #14 Jul 19 2017 20:39:43
%S 1,1,4,26,258,3346,54108,1054256,24161966,634230122,18806776982,
%T 622011916184,22754818956246,912075762692584,39755634279964662,
%U 1872279469323840472,94783193260373606758,5135585509536795416348,296656123838796109849526,18200829821539972354967252
%N Number of solid standard Young tableaux of cylindrical shape lambda X 2, where lambda ranges over all partitions of n.
%H S. B. Ekhad, D. Zeilberger, <a href="https://arxiv.org/abs/1202.6229">Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux</a>, arXiv:1202.6229v1 [math.CO], 2012
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%p b:= proc(l) option remember; local m; m:= nops(l);
%p `if`({map(x-> x[], l)[]}minus{0}={}, 1, add(add(`if`(l[i][j]>
%p `if`(i=m or nops(l[i+1])<j, 0, l[i+1][j]) and l[i][j]>
%p `if`(nops(l[i])=j, 0, l[i][j+1]), b(subsop(i=subsop(
%p j=l[i][j]-1, l[i]), l)), 0), j=1..nops(l[i])), i=1..m))
%p end:
%p g:= proc(n, i, l) `if`(n=0 or i=1, b(map(x->[2$x], [l[], 1$n])),
%p add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i))
%p end:
%p a:= n-> g(n, n, []):
%p seq(a(n), n=0..12);
%Y Column k=2 of A215204.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 07 2012
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