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

0,2

Links

Table of n, a(n) for n=0..20.

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

Prog

(PARI) a(n) = prod(k=0, n-1, 4*n-5*k);
(SageMath)
def a(n): return 5^n*falling_factorial(4*n/5, n)

Crossrefs

Cf. A061924, A343446.

Cf. A383997.

Sequence in context: A238299 A221656 A366623 * A339346 A214377 A331007

Adjacent sequences: A384239 A384240 A384241 * A384243 A384244 A384245

Keyword

sign,easy

Author

Seiichi Manyama, May 22 2025

Status

approved