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A175385 a(n) = numerator of sum{i=1..n} binomial(2n-i-1,i-1)/i. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.