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A092935
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a(1) = 1; a(n) = floor {(n+1)(n+2)(n+3)...(n+k)}/{(n-1)(n-2)(n-3)...(n-k)} for the least value of k.
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1
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1, 3, 2, 5, 14, 42, 6, 429, 1430, 4862, 16796, 58786, 2261, 742900, 2674440, 66861, 35357670, 129644790, 2274470, 1767263190, 25246617, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004
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OFFSET
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1,2
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COMMENTS
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The first occurrence of an integer in the sequence (n+1)/(n-1), (n+1)(n+2)/{(n-1)(n-2)}, (n+1)(n+2)(n+3)/{(n-1)(n-2)(n-3)},... The triangle of these numbers with initial value of n = 2, for k = 1 to n-1 is:
3
2 10
5/3 5 35
3/2 7/2 14 126
7/5 14/5 42/5 42 462
4/3 12/5 6 22 132 1716
...
Sequence contains the first integer in each row.
The leading diagonal of the triangle is given by A001700 = C(2n+1,n+1). i.e. eventually an integer occurs for k < n-1.
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LINKS
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EXAMPLE
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a(6)= 42: the relevant numbers are 7/5, 7*8/(5*4), 7*8*9/(5*4*3), (7*8*9*10)/(5*4*3*2),...or 1.4, 2.8,8.4,42,...
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PROG
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(PARI) { a(n) = local(p, q, r); p=1; q=1; for(k=1, n, p*=n+k; q*=n-k; r=gcd(p, q); p\=r; q\=r; if(q==1, break)); return(p) } (Alekseyev)
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CROSSREFS
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Sequence of corresponding values of k is A103634
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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