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A244299 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 5. 2
6, 21, 188, 791, 4696, 21614, 109745, 513421, 2557358, 11885545, 58291639, 275421640, 1342532532, 6411950652, 31310737486, 151220406569, 742729520457, 3625802212441, 17956348335989, 88575381634494, 442565032597013, 2207206278880826, 11138577085071310 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,1

COMMENTS

Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 5.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 7..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=5, `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=7..35);

MATHEMATICA

h[l_] := With[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j, l[[i]]}], {i, n}]];

g[n_, i_, l_] := Module[{j}, If[n == 0 || i < 1, 0, If[l != {} && l[[1]] - i == 5, If[j = Quotient[n, i]; Mod[n, i] == 0, h[Join[l, Table[i, {j}]]], 0], Sum[g[n - i*j, i - 1, Join[l, Table[i, {j}]]], {j, 0, n/i}]]]];

a[n_] := g[n, n, {}];

Table[a[n], {n, 7, 35}] (* Jean-Fran├žois Alcover, Aug 28 2021, after Maple code *)

CROSSREFS

Column k=5 of A238707.

Sequence in context: A210443 A179768 A131960 * A143049 A213680 A164643

Adjacent sequences:  A244296 A244297 A244298 * A244300 A244301 A244302

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jun 25 2014

STATUS

approved

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Last modified July 4 23:17 EDT 2022. Contains 355086 sequences. (Running on oeis4.)