cp's OEIS Frontend

E.g.f.: (hypergeom([1/3, 1/2], [], 36*x) - 3*hypergeom([1/6, 1/3], [], 36*x) + 2)/(3!*16).

a(n) = (2^n) * Product_{j=0..n-1} (3*j+1) * (-3*Product_{j=0..n-1} (6*j+1) + Product_{j=0..n-1} (6*j+3))/(3!*16), n>=2. From eq.12 of the Blasiak et al. reference with r=8, s=2, k=3.

a(n) = (2^(2*n-5)) * (3^(2*n-1)) * risefac(1/3, n) * (-3*risefac(1/6, n) + risefac(1/2, n)), n>=2, with risefac(x, n) = Pochhammer(x, n).

a(n) ~ sqrt(Pi) * 2^(2*n-4) * 3^(2*n-1) * n^(2*n-1/6) / (Gamma(1/3) * exp(2*n)). - Amiram Eldar, Aug 30 2025

a(n) = (2^(n-1))*Product_{j=0..n-1} ((3*j+1)*(6*j+1)), n>=1. From eq.12 of the Blasiak et al. reference with r=8, s=2, k=1.

a(n) = (6^(2*n))*risefac(1/6, n)*risefac(1/3, n)/2, n>=1, with risefac(x, n) = Pochhammer(x, n).

a(n) = fac6(6*n-5)*fac6(6*n-4)/2, n>=1, with fac6(6*n-5) = A008542(n) and fac6(6*n-4)/2 = A034689(n)= (2^(n-1))*A007559(n), (6-factorials).

a(n) ~ Pi * (6/e)^(2*n) * n^(2*n-1/2) / (Gamma(1/6) * Gamma(1/3)). - Amiram Eldar, Aug 30 2025

a(n)= sum( A092077(n, k)*(-1)^k, k=2..2*n), n>=1.

a(n)=sum(A092077(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+6*(j-1), 2), j=1..n), k=2..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=8, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.