login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..120

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-Fran├žois 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: A169790 A014009 A274220 * A288110 A085386 A290517

Adjacent sequences:  A218290 A218291 A218292 * A218294 A218295 A218296

KEYWORD

nonn

AUTHOR

Joerg Arndt, Oct 25 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 23 19:00 EST 2017. Contains 295128 sequences.