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 A007579 Number of Young tableaux of height <= 6. (Formerly M1217) 14
 1, 1, 2, 4, 10, 26, 76, 231, 756, 2556, 9096, 33231, 126060, 488488, 1948232, 7907185, 32831370, 138321690, 593610420, 2579109780, 11377862340, 50726936820, 229078351992, 1043999256966, 4810194384348, 22340617618860, 104742353862360, 494547143860035 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of n-length words w over 6-ary alphabet {a1,a2,...,a6} such that for every prefix z of w we have #(z,a1) >= #(z,a2) >= ... >= #(z,a6), where #(z,x) counts the letters x in word z. - Alois P. Heinz, May 30 2012 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 F. Bergeron, L. Favreau and D. Krob, Conjectures on the enumeration of tableaux of bounded height, Preprint. (Annotated scanned copy) F. Bergeron, L. Favreau and D. Krob, Conjectures on the enumeration of tableaux of bounded height, Discrete Math, vol. 139, no. 1-3 (1995), 463-468. Alon Regev, Amitai Regev, Doron Zeilberger, Identities in character tables of S_n, arXiv preprint arXiv:1507.03499 [math.CO], 2015. FORMULA a(n) ~ 3/4 * 6^(n+15/2)/(Pi^(3/2)*n^(15/2)). - Vaclav Kotesovec, Sep 11 2013 D-finite with recurrence +(n+5)*(n+9)*(n+8)*a(n) +4*(-5*n^2-46*n-84)*a(n-1) -4*(n-1)*(10*n^2+58*n+33)*a(n-2) +144*(n-1)*(n-2)*a(n-3) +144*(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Sep 23 2021 MAPLE h:= proc(l) local n; n:=nops(l); add(i, i=l)! /mul(mul(1+l[i]-j       +add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)     end: g:= proc(n, i, l) option remember;       `if`(n=0, h(l), `if`(i=1, h([l[], 1\$n]), `if`(i<1, 0,         g(n, i-1, l) +`if`(i>n, 0, g(n-i, i, [l[], i])))))     end: a:= n-> g(n, 6, []): seq(a(n), n=0..30); # Alois P. Heinz, Apr 18 2012 # second Maple program: a:= proc(n) option remember;       `if`(n<4, [1, 1, 2, 4][n+1], ((20*n^2+184*n+336)*a(n-1)        +4*(n-1)*(10*n^2+58*n+33)*a(n-2) -144*(n-1)*(n-2)*a(n-3)        -144*(n-1)*(n-2)*(n-3)*a(n-4))/ ((n+5)*(n+8)*(n+9)))     end: seq(a(n), n=0..30);  # Alois P. Heinz, Oct 12 2012 MATHEMATICA RecurrenceTable[{144 (-3+n) (-2+n) (-1+n) a[-4+n]+144 (-2+n) (-1+n) a[-3+n]-4 (-1+n) (33+58 n+10 n^2) a[-2+n]-4 (84+46 n+5 n^2) a[-1+n]+(5+n) (8+n) (9+n) a[n]==0, a[1]==1, a[2]==2, a[3]==4, a[4]==10}, a, {n, 20}] (* Vaclav Kotesovec, Sep 11 2013 *) CROSSREFS Column k=6 of A182172. - Alois P. Heinz, May 30 2012 Sequence in context: A294672 A239077 A148099 * A239078 A303930 A007123 Adjacent sequences:  A007576 A007577 A007578 * A007580 A007581 A007582 KEYWORD nonn AUTHOR EXTENSIONS More terms from Alois P. Heinz, Apr 10 2012 STATUS approved

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Last modified July 1 10:54 EDT 2022. Contains 354972 sequences. (Running on oeis4.)