A175386 a(n) = denominator of sum((1/i)*C(2n-i-1,i-1),i=1..n).

1, 2, 6, 4, 5, 4, 7, 8, 18, 10, 11, 24, 13, 14, 30, 16, 17, 12, 19, 20, 42, 22, 23, 48, 25, 26, 54, 28, 29, 20, 31, 32, 66, 34, 35, 72, 37, 38, 78, 40, 41, 28, 43, 44, 90, 46, 47, 96, 49, 50, 6, 52, 53, 36, 55, 56, 114, 58, 59, 120, 61, 62, 126, 64, 65, 44, 67, 68, 138, 70, 71

Offset: 1

Author

Zak Seidov, Vladimir Shevelev, Apr 24 2010

Keywords

• frac
• nonn

Comments

We conjecture that sum((1/i)*C(2n-i-1,i-1),i=1..n) is not an integer for n>1.

Crossrefs

Cf. A175385.

Programs

Mathematica

Table[Denominator[Sum[(1/i)*Binomial[2n-i-1,i-1],{i,1,n}]],{n,1,150}]

Formula

According to Mathematica, sum((1/i)*C(2n-i-1,i-1), i=1..n)=

(Hypergeometric2F1[1/2-n,-n,1-2 n,-4]-1)/(2 n).