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 A215123 Number of solid standard Young tableaux of shape [[n^2,n],[n]]. 3
 1, 2, 174, 52808, 31497284, 31113230148, 46190668836656, 96484621769643360, 270280816277448460968, 979042561410295182717884, 4456728497956906393963534248, 24916868994347706845906490576432, 167903137478620963997932010166057408 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..100 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 a(n) ~ exp(2*n+2) * n^(2*n-1) / (2*Pi). - Vaclav Kotesovec, Jan 19 2015 MAPLE b:= proc(x, y, z) option remember; `if`(zy and x>z, b(x-1, y, z), 0)+       `if`(y>0, b(x, y-1, z), 0)+ `if`(z>0, b(x, y, z-1), 0)))     end: a:= n-> b(n^2, n, n): seq(a(n), n=0..15); MATHEMATICA \$RecursionLimit = 1000; b[x_, y_, z_] :=  b[x, y, z] = If[zy && x>z, b[x-1, y, z], 0] + If[y>0, b[x, y-1, z], 0] + If[z>0, b[x, y, z-1], 0]]]; a[n_] := b[n^2, n, n]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 05 2015, after Alois P. Heinz *) CROSSREFS Central row elements of A215122. Main diagonal of A176129. Sequence in context: A281958 A172231 A193638 * A321634 A219724 A103427 Adjacent sequences:  A215120 A215121 A215122 * A215124 A215125 A215126 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 03 2012 STATUS approved

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Last modified July 22 07:23 EDT 2019. Contains 325216 sequences. (Running on oeis4.)