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A244300 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 6. 2
7, 28, 279, 1354, 8823, 45553, 256192, 1328368, 7272035, 37498159, 201732490, 1052038304, 5628260010, 29642509180, 158744001098, 844461334762, 4549886593291, 24435491901926, 132677029062176, 719558882421952, 3940213225673584, 21584248413514700 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,1

COMMENTS

Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 6.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..100

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) local j; `if`(n=0 or i<1, 0, `if`(l<>[] and

      l[1]-i=6, `if`(irem(n, i, 'j')=0, h([l[], i$j]), 0),

      add(g(n-i*j, i-1, [l[], i$j]), j=0..n/i)))

    end:

a:= n-> g(n$2, []):

seq(a(n), n=8..35);

CROSSREFS

Column k=6 of A238707.

Sequence in context: A054369 A185360 A198028 * A203209 A193288 A050548

Adjacent sequences:  A244297 A244298 A244299 * A244301 A244302 A244303

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jun 25 2014

STATUS

approved

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Last modified August 12 00:34 EDT 2022. Contains 356067 sequences. (Running on oeis4.)