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A215545
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Number of standard Young tableaux of shape [5n,5].
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2
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0, 42, 1638, 10659, 40480, 115101, 272272, 566618, 1072764, 1888460, 3137706, 4973877, 7582848, 11186119, 16043940, 22458436, 30776732, 41394078, 54756974, 71366295, 91780416, 116618337, 146562808, 182363454, 224839900, 274884896, 333467442, 401635913
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OFFSET
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0,2
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COMMENTS
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Also the number of binary words with 5n 1's and 5 0's such that for every prefix the number of 1's is >= the number of 0's.
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LINKS
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FORMULA
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G.f.: (4*x^5-24*x^4+256*x^3+1461*x^2+1386*x+42)*x/(x-1)^6.
a(n) = (5*n-4)*(5*n+2)*(5*n+3)*(5*n+4)*(n+1)/24 for n>0, a(0) = 0.
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MAPLE
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a:= n-> max(0, (5*n-4)*(5*n+2)*(5*n+3)*(5*n+4)*(n+1)/24):
seq(a(n), n=0..40);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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