diff --git a/ho_basis.jl b/ho_basis.jl
index 5948687..94f8547 100644
--- a/ho_basis.jl
+++ b/ho_basis.jl
@@ -4,11 +4,9 @@ using SpecialFunctions
 # Gaussian potentials in HO space
 inv_factorial(n) = Iterators.prod(inv.(1:n))
 sqrt_factorial(n) = Iterators.prod(sqrt.(n:-1:1))
-sqrt_double_factorial(n) = Iterators.prod(sqrt.(n:-2:1))
-N_nl(n, l) = (-1)^n * sqrt_factorial(n) * sqrt(1/sqrt(pi) * 2^(n+l+2)) / sqrt_double_factorial(2*n+2*l+1)
-prefactor(n, l, k) = (-1)^k * binomial(n + l + 1/2, n - k) * inv_factorial(k)
-Talmi(l, R, k1, k2) = (1/2) / (1 + 1/R^2)^(3/2 + l + k1 + k2) * gamma(3/2 + l + k1 + k2)
-V_Gaussian(R, l, n1, n2) = N_nl(n1, l) * N_nl(n2, l) * sum([prefactor(n1, l, k1) * prefactor(n2, l, k2) * Talmi(l, R, k1, k2) for (k1, k2) in Iterators.product(0:n1, 0:n2)])
+N_lnk(l, n, k) = (-1)^(n-k) * inv_factorial(k) * binomial(n+l+1/2, n-k) * sqrt_factorial(n) / sqrt(gamma(n+l+3/2))
+Talmi(l, R, k1, k2) = (1 + 1/R^2)^-(3/2 + l + k1 + k2) * gamma(3/2 + l + k1 + k2)
+V_Gaussian(R, l, n1, n2) = sum([N_lnk(l, n1, k1) * N_lnk(l, n2, k2) * Talmi(l, R, k1, k2) for (k1, k2) in Iterators.product(0:n1, 0:n2)])
 
 function get_sp_basis(E_max)
     Es = Int[]