A272395 Recurrence (of order 6):

 5*n*(2*n - 5)*(2*n - 3)*(3*n - 13)*(3*n - 10)*(3*n - 7)*(3*n - 4)*(5*n - 18)*(5*n - 13)*(5*n - 8)*(5*n - 7)*(5*n - 3)*(5*n - 2)*(5*n - 1)*(5*n + 1)*a(n) = 
 2*(n-1)*(2*n - 5)*(2*n - 1)*(3*n - 13)*(3*n - 10)*(3*n - 7)*(3*n - 2)*(3*n - 1)*(5*n - 18)*(5*n - 13)*(5*n - 8)*(5*n - 7)*(4651*n^3 - 14256*n^2 + 14408*n - 4800)*a(n-1)
 + 11*(n-1)*(2*n - 3)*(3*n - 13)*(3*n - 10)*(3*n - 4)*(5*n - 18)*(5*n - 13)*(5*n - 3)*(5*n - 2)*(45306*n^6 - 393711*n^5 + 1337179*n^4 - 2219861*n^3 + 1829843*n^2 - 672340*n + 89040)*a(n-2)
 - 242*(n-2)*(n-1)*(2*n - 5)*(2*n - 1)*(3*n - 13)*(3*n - 7)*(3*n - 2)*(3*n - 1)*(5*n - 18)*(5*n - 8)*(5*n - 7)*(2280*n^4 - 18133*n^3 + 49151*n^2 - 51862*n + 17664)*a(n-3)
 - 1331*(n-3)*(n-2)*(n-1)*(2*n - 3)*(3*n - 10)*(3*n - 4)*(3*n - 1)*(5*n - 13)*(5*n - 3)*(5*n - 2)*(5310*n^5 - 65811*n^4 + 301018*n^3 - 618557*n^2 + 546104*n - 147280)*a(n-4)
 + 29282*(n-4)*(n-3)*(n-2)*(n-1)*(2*n - 5)*(2*n - 1)*(3*n - 13)*(3*n - 7)*(3*n - 4)*(3*n - 2)*(3*n - 1)*(5*n - 18)*(5*n - 8)*(5*n - 7)*(5*n - 3)*a(n-5)
 + 161051*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(2*n - 3)*(2*n - 1)*(3*n - 10)*(3*n - 7)*(3*n - 4)*(3*n - 1)*(5*n - 13)*(5*n - 8)*(5*n - 3)*(5*n - 2)*a(n-6)