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 A215120 Number T(n,k) of solid standard Young tableaux of n cells and height >= k; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 2
 1, 1, 1, 3, 3, 1, 9, 9, 5, 1, 33, 33, 23, 7, 1, 135, 135, 109, 43, 9, 1, 633, 633, 557, 261, 69, 11, 1, 3207, 3207, 2975, 1641, 507, 101, 13, 1, 17589, 17589, 16825, 10503, 3787, 869, 139, 15, 1, 102627, 102627, 100007, 69077, 28205, 7487, 1369, 183, 17, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Rows n = 0..20, flattened S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012 Wikipedia, Young tableau FORMULA T(n,n) = 1, T(n,k) = T(n,k+1) + A214753(n,k) for k `if`(k=0, `if`(n=0, 1, 0), b(n, min(n, k), [])): H:= (n, k)-> A(n, k) -`if`(k=0, 0, A(n, k-1)): T:= proc(n, k) option remember; `if`(k=n, 1, T(n, k+1)+ H(n, k)) end: seq(seq(T(n, k), k=0..n), n=0..10); CROSSREFS Column k=0 gives: A207542. Diagonal and lower diagonal give: A000012, A005408. Cf. A214753, A215086. Sequence in context: A193741 A193824 A108075 * A084145 A122919 A188513 Adjacent sequences:  A215117 A215118 A215119 * A215121 A215122 A215123 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Aug 03 2012 STATUS approved

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Last modified June 16 07:14 EDT 2019. Contains 324145 sequences. (Running on oeis4.)