A175385 a(n) = numerator of Sum_{i=1..n} binomial(2n-i-1,i-1)/i.

1, 3, 17, 23, 61, 107, 421, 1103, 5777, 7563, 19801, 103681, 135721, 355323, 1860497, 2435423, 6376021, 11128427, 43701901, 114413063, 599074577, 784198803, 2053059121, 10749957121, 14071876561, 36840651123, 192900153617

Offset: 1

Author

Vladimir Shevelev, Zak Seidov, Apr 24 2010

Keywords

• nonn
• frac

Comments

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

Crossrefs

Cf. A175386 (denominator).

Programs

Mathematica

Table[Numerator[Sum[(1/i)*Binomial[2n-i-1,i-1],{i,1,n}]],{n,1,50}]

Formula

Sum_{i=1..n} C(2n-i-1,i-1)/i = (2F1(1/2-n,-n;1-2 n;-4) -1)/(2n), where 2F1 is the Gaussian Hypergeometric Function.