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A215544
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Number of standard Young tableaux of shape [4n,4].
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2
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0, 14, 275, 1260, 3705, 8602, 17199, 31000, 51765, 81510, 122507, 177284, 248625, 339570, 453415, 593712, 764269, 969150, 1212675, 1499420, 1834217, 2222154, 2668575, 3179080, 3759525, 4416022, 5154939, 5982900, 6906785, 7933730, 9071127, 10326624, 11708125
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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 4n 1's and 4 0's such that for every prefix the number of 1's is >= the number of 0's. The a(1) = 14 words are: 10101010, 10101100, 10110010, 10110100, 10111000, 11001010, 11001100, 11010010, 11010100, 11011000, 11100010, 11100100, 11101000, 11110000.
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LINKS
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FORMULA
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G.f.: (3*x^4-15*x^3-25*x^2-205*x-14)*x/(x-1)^5.
a(n) = (4*n-3)*(4*n+3)*(2*n+1)*(n+1)/3 for n>0, a(0) = 0.
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MAPLE
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a:= n-> max(0, (4*n+3)*(2*n+1)*(4*n-3)*(n+1)/3):
seq(a(n), n=0..40);
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MATHEMATICA
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LinearRecurrence[{5, -10, 10, -5, 1}, {0, 14, 275, 1260, 3705, 8602}, 40] (* Harvey P. Dale, Jan 25 2024 *)
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PROG
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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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