cp's OEIS Frontend

a(n) = Sum_{k=0..n} C(2, 2; k)*C(2, 2; n-k).

G.f.: ((3+c(4*x))/(2*(1-2*x*c(4*x))*(1+c(4*x))))^2, with c(x) g.f. for A000108 (Catalan). Also: (c(4*x)*(3+c(4*x)))^2/(1+c(4*x))^4, or (-1+36*x +(1+24*x)*c(4*x))/((1-4*x)*(1+20*x)*c(4*x)-1+44*x-16*x^2).

a(n) = A067297(2n).

G.f.: A(x) = (f(y) + f(-y))/2 with f(y) := (-1 + 9*y + (1+6*y)*c(y))/((1-y)*(1+5*y)*c(y) - 1 + 11*y - y^2) where c(y) is g.f. of A000108 (Catalan) and y=4*sqrt(x).

a(n) = A067302(2n+1) = (2*n+3)*A067297(2*n+1)/2.

G.f.: A(x) = (2*x*(d/dx)g(x) + 3*g(x)) with g(x) g.f. of A067321.