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.
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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Mar 22 2004
EXTENSIONS
More terms from Max Alekseyev, Feb 11 2005
STATUS
approved