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A244298 Number of standard Young tableaux with n cells such that the lengths of the first and the last row differ by 4. 2
5, 15, 119, 421, 2254, 8999, 40349, 166817, 737829, 3008774, 13186593, 54944783, 238422808, 1010671048, 4395831546, 18821162274, 82799233661, 359711480525, 1599420076729, 7030074945271, 31626819884986, 141486845119777, 646988113794544, 2940338763342920 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

COMMENTS

Also the number of ballot sequences of length n such that the multiplicities of the largest and the smallest value differ by 4.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..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=4, `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=6..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 == 4, 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, 6, 35}] (* Jean-François Alcover, Aug 28 2021, after Maple code *)

CROSSREFS

Column k=4 of A238707.

Sequence in context: A220825 A303230 A173736 * A050542 A091096 A116957

Adjacent sequences:  A244295 A244296 A244297 * A244299 A244300 A244301

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jun 25 2014

STATUS

approved

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Last modified August 12 23:52 EDT 2022. Contains 356077 sequences. (Running on oeis4.)