A215301 Number of solid standard Young tableaux of shape [[n,n-5],[5]].

42, 1452, 22689, 245962, 2149454, 16290708, 111709178, 711996820, 4292788212, 24777783256, 138077129921, 747501664986, 3949741123174, 20444004524804, 103955714523390, 520494659493180, 2570907398453580, 12546842041060200, 60579487688891610, 289692893191143876

Offset: 5

Author

Alois P. Heinz, Aug 07 2012

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..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

Crossrefs

Column k=5 of A214775.

Cf. A215002.

Programs

Maple

a:=proc(n) option remember; `if`(n<7, [0$4, 42, 1452, 22689][n],
   ((-940984202308081409937789248*n^7+36378423601372783158274124928*n^6
    -540987251973268278464961515672*n^5+4140452478540141056223108638628*n^4
    -17643038551017281385645661643624*n^3+40489345935054116443261823323140*n^2
    -39934974057986427003556989745680*n-247683783218781902433156798480)*a(n-1)
    +(5038765510419498883689330496*n^7-154613008671019208064714735488*n^6
    +1939670093038831522623368803072*n^5-12888788321486668402366527701360*n^4
+48941495657518683977159471709724*n^3-105016281014420890409086708155812*n^2
    +113403222542936117699329884355248*n-47046838608769352958257951122560)
    *a(n-2))/(79676793824198327746135844*n^7-1949805875384464242394656236*n^6
    +20900166698905174940775960603*n^5-125515785015357799830976856812*n^4
    +431332553464051479008795376439*n^3-723271251684163430971195319466*n^2
    +59211568171613916060478086240*n+1362260807703300463382362391640))
   end:
seq(a(n), n=5..30);

Mathematica

Flatten[{42, 1452, Table[(2*(n-6))! / (5 * (n-6)! * (n+1)!) * 64 * (-51975 + 217350*n - 873908*n^2 + 1738396*n^3 - 2038350*n^4 + 1500940*n^5 - 724004*n^6 + 231788*n^7 - 48750*n^8 + 6460*n^9 - 488*n^10 + 16*n^11), {n, 7, 20}]}]

Formula

See Maple program.

For n > 6, a(n) = (2*(n-6))! / (5 * (n-6)! * (n+1)!) * 64 * (-51975 + 217350*n - 873908*n^2 + 1738396*n^3 - 2038350*n^4 + 1500940*n^5 - 724004*n^6 + 231788*n^7 - 48750*n^8 + 6460*n^9 - 488*n^10 + 16*n^11). - Vaclav Kotesovec, Sep 02 2014