a(n) = Sum_{j=0..n, j even} binomial(n, j) * oddfactorial(j/2) * n^j, where oddfactorial(n) = (2*n)! / (2^n*n!).

A359739

a(n) = Sum_{j=0..n, j even} binomial(n, j) * oddfactorial(j/2) * n^j, where oddfactorial(n) = (2*n)! / (2^n*n!).