A050149 a(n) = T(n,n-3), array T as in A050143.

1, 15, 80, 432, 2352, 12896, 71136, 394400, 2196128, 12273648, 68811184, 386838480, 2179890000, 12309739968, 69641542848, 394643939904, 2239678552640, 12727572969680, 72415319422992, 412470467298032

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Formula

a(n) = Sum_{s=1..n} binomial(n,s)*binomial(s+n-5,n-4) = n*hypergeom([-n + 1, n-3], [2], -1) for n >= 4 and a(1) = 1. - Petros Hadjicostas, Feb 14 2021

D-finite with recurrence 3*(n-1)*(n-4)*a(n) +(-23*n^2+139*n-180)*a(n-1) +3*(11*n^2-91*n+170)*a(n-2) -5*(n-2)*(n-7)*a(n-3)=0 for n-3>=4. - R. J. Mathar, Jul 31 2025