A109074 Numerator of binomial(6*n-2,2*n)/(2*binomial(4*n-1,2*n)).

1, 1, 3, 26, 323, 2415, 26970, 66526, 717541, 278992987, 30741431, 753069156, 21291561634, 1258540885373, 11255629805034, 833378477982, 181778972767041, 101220208716435, 644821697046585, 4759584409762049637, 7692170694126370209, 19898042621084590853

Offset: 0

Author

N. J. A. Sloane, May 04 2008

Keywords

• nonn
• frac

Comments

It is conjectured that binomial(6*n-2,2*n)/(2*binomial(4*n-1,2*n)) = A005156(n+1)/A005156(n).

Examples

			1/2, 1, 3, 26/3, 323/13, 2415/34, 26970/133, 66526/115, 717541/435, 278992987/59334, 30741431/2294, ...
		

References

• D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; see conjecture (6.18).

Crossrefs

Cf. A134357, A005156.

Programs

Mathematica

Table[Numerator[Binomial[6n-2,2n]/(2Binomial[4n-1,2n])],{n,0,30}] (* Harvey P. Dale, Sep 29 2024 *)