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, 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

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

Table of n, a(n) for n=1..28.

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