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 A007580 Number of Young tableaux of height <= 8. (Formerly M1220) 10
 1, 1, 2, 4, 10, 26, 76, 232, 764, 2619, 9486, 35596, 139392, 562848, 2352064, 10092160, 44546320, 201158620, 930213752, 4387327088, 21115314916, 103386386516, 515097746072, 2605341147472, 13378787264584, 69622529312665, 367161088308490, 1959294979429380 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of n-length words w over 8-ary alphabet {a1,a2,...,a8} such that for every prefix z of w we have #(z,a1) >= #(z,a2) >= ... >= #(z,a8), 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. FORMULA a(n) ~ 135/16 * 8^(n+14)/(Pi^2*n^14). - Vaclav Kotesovec, Sep 11 2013 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, 8, []): seq(a(n), n=0..30); # Alois P. Heinz, Apr 10 2012 # second Maple program: a:= proc(n) option remember;       `if`(n<4, [1, 1, 2, 4][n+1],        ((40*n^3+1084*n^2+8684*n+18480)*a(n-1)        +16*(n-1)*(5*n^3+107*n^2+610*n+600)*a(n-2)        -1024*(n-1)*(n-2)*(n+6)*a(n-3)        -1024*(n-1)*(n-2)*(n-3)*(n+4)*a(n-4)) /        ((n+7)*(n+12)*(n+15)*(n+16)))     end: seq(a(n), n=0..30);  # Alois P. Heinz, Oct 12 2012 MATHEMATICA RecurrenceTable[{1024 (-3+n) (-2+n) (-1+n) (4+n) a[-4+n]+1024 (-2+n) (-1+n) (6+n) a[-3+n]-16 (-1+n) (600+610 n+107 n^2+5 n^3) a[-2+n]-4 (4620+2171 n+271 n^2+10 n^3) a[-1+n]+(7+n) (12+n) (15+n) (16+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=8 of A182172. - Alois P. Heinz, May 30 2012 Sequence in context: A220871 A007578 A239079 * A239080 A212915 A239081 Adjacent sequences:  A007577 A007578 A007579 * A007581 A007582 A007583 KEYWORD nonn AUTHOR EXTENSIONS More terms from Alois P. Heinz, Apr 10 2012 STATUS approved

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Last modified May 13 18:08 EDT 2021. Contains 343865 sequences. (Running on oeis4.)