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 A092935 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS EXAMPLE 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,... PROG (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) CROSSREFS Cf. A001700. Sequence of corresponding values of k is A103634 Sequence in context: A290427 A265759 A057674 * A137455 A111273 A068553 Adjacent sequences:  A092932 A092933 A092934 * A092936 A092937 A092938 KEYWORD nonn AUTHOR Amarnath Murthy, Mar 22 2004 EXTENSIONS More terms from Max Alekseyev, Feb 11 2005 STATUS approved

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)