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

1,2

Comments

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

Links

Table of n, a(n) for n=1..27.

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.

Mathematica

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

Crossrefs

Cf. A175386 (denominator).

Sequence in context: A206626 A128107 A154620 * A174268 A273834 A273850

Adjacent sequences: A175382 A175383 A175384 * A175386 A175387 A175388

Keyword

nonn,frac

Author

Vladimir Shevelev, Zak Seidov, Apr 24 2010

Status

approved