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A215688 Number of solid standard Young tableaux of shape [[3*n,3],[3]]. 2
0, 192, 7020, 52808, 229680, 738192, 1950512, 4488180, 9314448, 17841200, 32050452, 54630432, 89126240, 140105088, 213336120, 315984812, 456821952, 646447200, 897527228, 1225048440, 1646584272, 2182577072, 2856634560, 3695840868, 4731082160, 5997386832 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012
Wikipedia, Young tableau
FORMULA
G.f.: 4*(8*x^6-41*x^5+105*x^4+181*x^3+1925*x^2+1419*x+48)*x/(1-x)^7.
a(n) = (3*n-1)*(3*n-2)*(3*n^2+13*n+16)*(3*n^2+5*n+4)/4 for n>0, a(0) = 0.
MAPLE
a:= n-> `if`(n=0, 0, 32+(-312+(-362+(171+(657+(405+81*n)*n)*n)*n)*n)*n/4):
seq(a(n), n=0..40);
CROSSREFS
Row n=3 of A176129.
Sequence in context: A233154 A292076 A223214 * A173783 A290178 A282208
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 20 2012
STATUS
approved

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Last modified July 23 19:43 EDT 2024. Contains 374553 sequences. (Running on oeis4.)