A384216 -id:A384216 - cp's OEIS frontend

A383996 a(n) = Product_{k=0..n-1} (n-4*k).

1, 1, -4, 15, 0, -1155, 20160, -208845, 0, 68139225, -2075673600, 34976316375, 0, -25949801752875, 1126343522304000, -26264240610733125, 0, 34770736214117528625, -1958486116582195200000, 58318039100493206409375, 0, -120842042784862988395681875, 8366746697372733839769600000

Offset: 0

Seiichi Manyama, May 22 2025

Column k=4 of A384216.

Cf. A303487.

PARI
```
a(n) = prod(k=0, n-1, n-4*k);
```

def a(n): return 4^n*falling_factorial(n/4, n)

a(n) = 4^n * FallingFactorial(n/4,n).
a(n) = n! * [x^n] (1 + 4*x)^(n/4).
a(4*n) = 0 for n > 0.

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

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, May 22 2025

Column k=5 of A384216.

Cf. A303488.

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

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

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.

cp's OEIS Frontend

A383996 a(n) = Product_{k=0..n-1} (n-4*k).

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