a[n_] := Sum[Binomial[6 n, n + k] Binomial[4 n, k] (-1)^k, {k, 0, 4 n}] zero[n_] := Binomial[3 n, n] Binomial[6 n, 3 n] - Binomial[5 n, n] a[n] zero /@ Range[0, 10] See also: https://oeis.org/A304126 ( nice! ) In terms of OEIS numbering, A304126 neither divides A005809 nor A066802, yet it does divide their product A113424. This can be proven using Zeilberger's algorithm, or via ExpToODE according to the integral definition, a_n = 1/(2*pi) Int_{0..2*Pi} (2^10*cos(x)^6*sin(x)^4)^n *dx . More on this soon... --Brad