A384242 a(n) = Product_{k=0..n-1} (4*n-5*k).
1, 4, 24, 168, 1056, 0, -229824, -7233408, -162860544, -2573835264, 0, 2333140153344, 131053381595136, 4948323499671552, 124773727026364416, 0, -256422032696998232064, -20710128948965418074112, -1096668276542495972130816, -37948699305215165278715904, 0
Offset: 0
Programs
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PARI
a(n) = prod(k=0, n-1, 4*n-5*k);
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Sage
def a(n): return 5^n*falling_factorial(4*n/5, n)
Formula
a(n) = 5^n * FallingFactorial(4*n/5,n).
a(n) = n! * [x^n] (1 + 5*x)^(4*n/5).
a(n) = 4 * (-1)^(n-1) * A383997(n) for n > 0.
a(5*n) = 0 for n > 0.
D-finite with recurrence a(n) +8*n*(4*n-15)*(4*n-5)*(n-5)*(2*n-5)*a(n-5)=0. - R. J. Mathar, May 26 2025