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
Programs
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PARI
a(n) = prod(k=0, n-1, n-4*k);
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Sage
def a(n): return 4^n*falling_factorial(n/4, n)
Formula
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.