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A359175
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a(n) = binomial(2*n-2,n) - 2*(n-1).
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0
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0, 9, 48, 200, 780, 2989, 11424, 43740, 167940, 646624, 2496120, 9657674, 37442132, 145422645, 565722688, 2203961396, 8597496564, 33578000572, 131282408360, 513791607378, 2012616400036, 7890371113904, 30957699535728
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OFFSET
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3,2
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COMMENTS
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a(n) is the number of ways to place n indistinguishable balls into n-1 distinguishable boxes with at least one box remaining empty and not all balls placed in one box.
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LINKS
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FORMULA
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a(n) = A001791(n-1) - 2*(n-1), n > 2.
G.f.: (x^4 - 2*x^3 - 2*x^2 + 2*x - 1)/(1 - x)^2 + 4*x^2/(sqrt(1 - 4*x)*(sqrt(1 - 4*x) - 1)^2). - Stefano Spezia, Dec 28 2022
D-finite with recurrence n*a(n) +7*(-n+1)*a(n-1) +2*(7*n-16)*a(n-2) +4*(-2*n+7)*a(n-3) +12*(n-5)=0. - R. J. Mathar, Jan 25 2023
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EXAMPLE
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For n=4, the 9 distributions are:
|ooo|o| |
|ooo| |o|
|o|ooo| |
| |ooo|o|
|o| |ooo|
| |o|ooo|
|oo|oo| |
|oo| |oo|
| |oo|oo|.
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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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