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A251702
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a(1)=5, a(n) = a(n-1)*(a(n-1)-1)*(a(n-1)-2)/6.
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5
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OFFSET
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1,1
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COMMENTS
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In general, sequence a(n) = binomial(a(n-1),k) is asymptotic to (k!)^(1/(k-1)) * c^(k^n), where the constant c is dependent on k and a(1). For big a(1), c asymptotically approaches (a(1)/(k!)^(1/(k-1)))^(1/k). - Vaclav Kotesovec, Dec 09 2014
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LINKS
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FORMULA
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Limit_{n->oo} a(n)^(1/3^n) = 1.1546796279605837888382808629570944052320556413... (see A251792).
a(n) = binomial(a(n-1),3) for n >= 1. - Shel Kaphan, Feb 06 2023
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EXAMPLE
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a(2) = a(1)*(a(1)-1)*(a(1)-2)/6 = 5*4*3/6 = 10.
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MATHEMATICA
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RecurrenceTable[{a[1] == 5, a[n] == a[n - 1](a[n - 1] - 1)(a[n - 1] - 2)/6}, a[n], {n, 10}]
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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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