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A244301 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 7. 2
8, 36, 395, 2166, 15365, 87515, 537860, 3043387, 18079805, 101484440, 590719670, 3340021038, 19305133044, 110029379692, 636377579038, 3658493392345, 21277586564634, 123462793881974, 723417146721998, 4238255849152496, 25044116796884830, 148185594856438664 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,1

COMMENTS

Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 7.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 9..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=7, `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=9..35);

CROSSREFS

Column k=7 of A238707.

Sequence in context: A203297 A181072 A058823 * A268157 A203020 A276175

Adjacent sequences:  A244298 A244299 A244300 * A244302 A244303 A244304

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jun 25 2014

STATUS

approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)