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a(n) = Product_{j=0..n-1} ((5*j+2)*(5*j+1))/2, n>=1. From eq.12 of the Blasiak et al. reference with r=7, s=2, k=1.

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

a(n) = fac5(5*n-3)*fac5(5*n-4)/2, n>=1, with fac5(5*n-4)/2 = A034323(n) and fac5(5*n-3) = A008548(n) (5-factorials).

E.g.f.: (hypergeom([1/5, 2/5], [], 25*x)-1)/2.

a(n) = A091747(n, 2), n>=1.

D-finite with recurrence a(n) - (5*n-3)*(5*n-4)*a(n-1) = 0. - R. J. Mathar, Jul 27 2022

a(n) ~ Pi * (5/e)^(2*n) * n^(2*n-2/5) / (Gamma(1/5) * Gamma(2/5)). - Amiram Eldar, Sep 01 2025

a(n) ~ sqrt(Pi*(1 + sqrt(5))) * 5^(2*n + 1/4) * n^(2*n - 2/5) / (Gamma(1/10) * 2^(7/10) * exp(2*n)). - Vaclav Kotesovec, Sep 01 2025

a(n)=sum(A091747(n, k)*(-1)^k, k=2..2*n), n>=1.

a(n, k) = (((-1)^k)/k!)*sum(((-1)^p)*binomial(k, p)*product(fallfac(p+6*(j-1), 2), j=1..n), p=2..k), n>=1, 2<=k<=2*n, else 0. From eq. (12) of the Blasiak et al. reference with r=8, s=2.

Recursion: a(n, k) = sum(binomial(2, p)*fallfac(6*(n-1)+k-p, 2-p)*a(n-1, k-p), p=0..2), n>=2, 2<=k<=2*n, a(1, 2)=1, else 0. Rewritten from eq.(19) of the Schork reference with r=8, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle).

a(n)=sum(A091747(n, k), k=2..2*n)= sum((1/k!)*product(fallfac(k+5*(j-1), 2), j=1..n), k=2..infinity)/exp(1), n>=1. From eq.(9) of the Blasiak et al. reference with r=7, s=2. fallfac(n, m) := A008279(n, m) (falling factorials triangle). a(0) := 1 may be added.