login
A218293
Number of standard Young tableaux with shapes corresponding to partitions into distinct parts.
14
1, 1, 1, 3, 4, 10, 31, 70, 190, 561, 2191, 6226, 22683, 74152, 283349, 1211354, 4572672, 18844177, 77585825, 327472752, 1418056071, 7083303437, 31251988918, 153456264178, 723293387594, 3596567095155, 17360616601051, 89955643932801, 486526881887485, 2551613423040841, 14029592127656040, 76756835252971657, 428044848852530252
OFFSET
0,4
LINKS
Wikipedia, Young tableau
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 s; s:=i*(i+1)/2;
`if`(n=s, h([l[], seq(i-j, j=0..i-1)]), `if`(n>s, 0,
g(n, i-1, l)+ `if`(i>n, 0, g(n-i, i-1, [l[], i]))))
end:
a:= n-> g(n, n, []):
seq(a(n), n=0..40); # Alois P. Heinz, Nov 08 2012
MATHEMATICA
h[l_List] := Module[{n=Length[l]}, Total[l]!/Product[Product[1+l[[i]]-j + Sum[ If[ l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}]]; g[n_, i_, l_List] := Module[{s=i*(i+1)/2}, If[n == s, h[Join[l, Table[i-j, {j, 0, i-1}]]], If[n > s, 0, g[n, i-1, l] + If[i>n, 0, g[n-i, i-1, Append[l, i]]]]]]; a[n_] := g[n, n, {}]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 18 2015, after Alois P. Heinz *)
CROSSREFS
Cf. A000085 (standard Young tableaux for all shapes).
Diagonal of A219272, row sums of A219274, A219311. - Alois P. Heinz, Nov 17 2012
Cf. A225121 (tableaux with shapes corresponding to partitions into distinct parts with minimal difference 2).
Sequence in context: A014009 A274220 A299881 * A374313 A288110 A085386
KEYWORD
nonn
AUTHOR
Joerg Arndt, Oct 25 2012
STATUS
approved