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 A293128 Number of standard Young tableaux of 2n cells and height <= n. 4
 1, 1, 6, 51, 588, 7990, 126060, 2242618, 44546320, 977152266, 23500234512, 615372604033, 17442275104496, 532242021137346, 17399782340548920, 606732491690590816, 22477989291826848000, 881635273413199806994, 36493478646922003374096, 1589642562747880936613248 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of standard Young tableaux of 2n cells and <= n columns. Also the number of 2n-length words w over n-ary alphabet {a1,a2,...,an} such that for every prefix z of w we have #(z,a1) >= #(z,a2) >= ... >= #(z,an), where #(z,x) counts the letters x in word z. The a(2) = 6 words of length 4 over alphabet {a,b} are: aaaa, aaab, aaba, abaa, aabb, abab. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..41 (terms 0..32 from Alois P. Heinz) Wikipedia, Young tableau FORMULA a(n) = A182172(2n,n). MAPLE h:= l-> (n-> add(i, i=l)!/mul(mul(1+l[i]-j+add(`if`(l[k]       `if`(n=0 or i=1, h([l[], 1\$n]), add(                g(n-i*j, i-1, [l[], i\$j]), j=0..n/i)): a:= n-> g(2*n, n, []): seq(a(n), n=0..15); MATHEMATICA h[l_] := With[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] < j, 0, 1], {k, i + 1, n}], {j, 1, l[[i]]}], {i, 1, n}]]; g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Table[1, {n}]]], Sum[g[n - i*j, i - 1, Join[l, Table[i, {j}]]], {j, 0, n/i}]]; a[n_] := g[2n, n, {}]; a /@ Range[0, 15] (* Jean-François Alcover, Jan 02 2021, after Alois P. Heinz *) CROSSREFS Cf. A182172, A267436. Sequence in context: A113352 A063169 A246189 * A304185 A215003 A134525 Adjacent sequences:  A293125 A293126 A293127 * A293129 A293130 A293131 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 30 2017 STATUS approved

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Last modified June 22 09:57 EDT 2021. Contains 345375 sequences. (Running on oeis4.)