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 A215300 Number of solid standard Young tableaux of shape [[n,n-4],[4]]. 2
 14, 378, 4804, 43573, 325590, 2149454, 13054108, 74688594, 408634828, 2159302420, 11097147528, 55747502501, 274790652518, 1332928973766, 6377276361900, 30149660760870, 141057202034340, 653892592144620, 3006490865152440, 13722387184879650, 62220533305358076 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 4..500 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 See Maple program. For n > 4, a(n) = (2*(n-5))!/(3*(n-5)!*(n+1)!)*(160*(-567 + 2394*n - 8862*n^2 + 15592*n^3 - 15484*n^4 + 9152*n^5 - 3292*n^6 + 704*n^7 - 82*n^8 + 4*n^9)). - Vaclav Kotesovec, Sep 02 2014 MAPLE a:= proc(n) option remember; `if`(n<6, [0\$3, 14, 378, 4804][n],       ((-460961029024*n^4 +54902186125572*n^3 -347074341314956*n^2        +421934757637074*n +6838164520124) *a(n-1) +(104238656896016*n^4        -2317913124589048*n^3 +16535317231755832*n^2 -44274446438628908*n        +29901662719961532)*a(n-2) +(-391233321452352*n^4        +7447800734464704*n^3 -48294258553516272*n^2 +122447135865649584*n        -105955729051546080)*a(n-3)) / (286655151052*n^4 -1210962058579*n^3        +4322649356693*n^2 -24951473774234*n -30771740340558))     end: seq(a(n), n=4..30); MATHEMATICA Flatten[{14, Table[(2*(n-5))!/(3*(n-5)!*(n+1)!)*(160*(-567+2394*n-8862*n^2+15592*n^3-15484*n^4+9152*n^5-3292*n^6+704*n^7-82*n^8+4*n^9)), {n, 5, 20}]}] (* Vaclav Kotesovec, Sep 02 2014 *) CROSSREFS Column k=4 of A214775. Cf. A215002. Sequence in context: A113673 A184268 A223383 * A159535 A171718 A270409 Adjacent sequences:  A215297 A215298 A215299 * A215301 A215302 A215303 KEYWORD nonn AUTHOR Alois P. Heinz, Aug 07 2012 STATUS approved

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Last modified May 22 19:46 EDT 2019. Contains 323481 sequences. (Running on oeis4.)