A211505 Number of solid standard Young tableaux of shape [[(3)^n],[3]].

5, 192, 5471, 143164, 3636776, 91442364, 2293620329, 57583680440, 1449149180310, 36577522323264, 926132803592304, 23521922685452320, 599176262762762880, 15305331537941936820, 391972832520910172865, 10062682947669846370800, 258904473727824391312650

Offset: 1

Author

Alois P. Heinz, Aug 06 2012

Keywords

• nonn

Comments

a(n) is odd if and only if n = 2^k-1, k in {1, 2, 3, ... }.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..700
• S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012
• Wikipedia, Young tableau

Crossrefs

Row n=3 of A214722.

Cf. A000225.

Programs

Maple

a:=proc(n) option remember; `if`(n<3, [5, 192][n],
   ((-300307980720421134*n^6 -450257143569814251*n^5 +520721206232593545*n^4
    +237675576478617990*n^3 -244917832991741721*n^2 +20947752092648421*n
    +7263907687560150)*a(n-2) +(20284627624231332*n^6 +74969736339564876*n^5
    -90577816139486502*n^4 -578021108537112633*n^3 -713543105276625459*n^2
    -309855589348004634*n -29055630750240600)*a(n-1)) / (339337400732270*n^6
    +2086412513047793*n^5 -1761594949059583*n^4 -24340927184757907*n^3
    -25005499944921313*n^2 +25705682578023740*n +29939073413286900))
   end:
seq(a(n), n=1..20);

Mathematica

Table[(600 + 2874*n + 4709*n^2 + 3246*n^3 + 1019*n^4 + 144*n^5 + 8*n^6)*(2+3*n)! / (2*(3+2*n)*(5+2*n)*(n-1)!*(2+n)!*(5+n)!), {n, 1, 20}] (* Vaclav Kotesovec, Jul 16 2014 *)

Formula

a(n) = (600 + 2874*n + 4709*n^2 + 3246*n^3 + 1019*n^4 + 144*n^5 + 8*n^6)*(2+3*n)! / (2*(3+2*n)*(5+2*n)*(n-1)!*(2+n)!*(5+n)!). - Vaclav Kotesovec, Jul 16 2014