A383997 a(n) = Product_{k=0..n-1} (n-5*k).

1, 1, -6, 42, -264, 0, 57456, -1808352, 40715136, -643458816, 0, 583285038336, -32763345398784, 1237080874917888, -31193431756591104, 0, 64105508174249558016, -5177532237241354518528, 274167069135623993032704, -9487174826303791319678976, 0

Offset: 0

Author

Seiichi Manyama, May 22 2025

Keywords

• sign
• easy

Crossrefs

Column k=5 of A384216.

Cf. A303488.

Programs

PARI

a(n) = prod(k=0, n-1, n-5*k);

Sage

def a(n): return 5^n*falling_factorial(n/5, n)

Formula

a(n) = 5^n * FallingFactorial(n/5,n).

a(n) = n! * [x^n] (1 + 5*x)^(n/5).

a(5*n) = 0 for n > 0.