cp's OEIS Frontend

a(n) = n! * Sum_{k=0..n} (n-k+1)^(k-1) * binomial(n+2*k-1,n-k)/k!.

a(n) ~ sqrt(s*(1 + 2*r*s) / (4 + 3*r - 12*r*s + 12*r^2*s^2 - 4*r^3*s^3)) * n^(n-1) / (exp(n) * r^n), where r = 0.1811100305436879929789759231994897963241226689... and s = 1.893740207738561813713992833266450862854198944672... are real roots of the system of equations exp(r/(1 - r*s)^3) = s, 3*s*r^2 = (1 - r*s)^4. - Vaclav Kotesovec, Nov 18 2023

a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(n+k-1,n-k)/k!.

a(n) ~ s^2 * sqrt((1 + r*s)/(1 + 2*r*s^2 - 3*r^2*s^2 + 2*r^3*s^3)) * n^(n-1) / (exp(n) * r^(n - 1/2)), where r = 0.1208150626316801846776206051780724146363... and s = 1.505405324736640697527292770220289316454393380356... are real roots of the system of equations exp(r*s^2 / (1 - r*s)^2) = s, 2*r*s^2 = (1 - r*s)^3. - Vaclav Kotesovec, Nov 18 2023

a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(3*k,n-k)/k!.