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A215550
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Number of standard Young tableaux of shape [10n,10].
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2
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0, 16796, 15737865, 574221648, 7766844470, 60610884906, 331670995656, 1414591812920, 5014392953273, 15408077648040, 42254306265171, 105611585968616, 244384627765200, 529868222188998, 1086607184873210, 2123449623259536, 3978448975695051, 7182177974166580
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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 10n 1's and 10 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.: (9*x^10 -99*x^9 -140503*x^8 -25387417*x^7 -510202946*x^6 -2566871318*x^5 -4166581331*x^4 -2313217577*x^3 -402028913*x^2 -15553109*x -16796)*x / (x-1)^11.
a(n) = C(10*n+10,10)*(10*n-9)/(10*n+1) for n>0, a(0) = 0.
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MAPLE
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a:= n-> max(0, binomial(10*n+10, 10)*(10*n-9)/(10*n+1)):
seq(a(n), n=0..30);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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