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A126596
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a(n) = binomial(4*n,n)*(2*n+1)/(3*n+1).
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7
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1, 3, 20, 154, 1260, 10659, 92092, 807300, 7152444, 63882940, 574221648, 5188082354, 47073334100, 428634152730, 3914819231400, 35848190542920, 329007937216860, 3025582795190340, 27872496751392496, 257172019222240200, 2376196095585231920, 21983235825545286435
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OFFSET
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0,2
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COMMENTS
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Number of standard Young tableaux of shape [3n,n]. Also the number of binary words with 3n 1's and n 0's such that for every prefix the number of 1's is >= the number of 0's. The a(1) = 3 words are: 1011, 1101, 1110. - Alois P. Heinz, Aug 15 2012
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LINKS
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FORMULA
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a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(2*n+1). - Ilya Gutkovskiy, Nov 01 2017
Recurrence: 3*n*(3*n-1)*(3*n+1)*a(n) = 8*(2*n+1)*(4*n-3)*(4*n-1)*a(n-1). - Vaclav Kotesovec, Feb 03 2018
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MAPLE
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seq((2*n+1)*binomial(4*n, n)/(3*n+1), n=0..22); # Emeric Deutsch, Mar 27 2007
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MATHEMATICA
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Table[(Binomial[4n, n](2n+1))/(3n+1), {n, 0, 30}] (* Harvey P. Dale, Feb 06 2016 *)
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PROG
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(Magma) [Binomial(4*n, n)*(2*n+1)/(3*n+1): n in [0..20]]; // Vincenzo Librandi, Nov 18 2011
(Haskell)
a126596 n = a005810 n * a005408 n `div` a016777 n
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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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EXTENSIONS
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STATUS
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approved
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