A384259 - OEIS

A384259

a(n) = Product_{k=0..n-1} (n+4*k+3).

1, 4, 45, 840, 21945, 737280, 30282525, 1470268800, 82380323025, 5231974809600, 371413503586125, 29144138639616000, 2504851570980383625, 234017443515727872000, 23613335889752371888125, 2559272716623604101120000, 296519181502679448839150625, 36572320958219876869079040000

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = 4^n * RisingFactorial((n+3)/4,n).

a(n) = n! * [x^n] 1/(1 - 4*x)^((n+3)/4).

D-finite with recurrence a(n) -5*(5*n-9)*(5*n-13)*(5*n-1)*(5*n-17)*a(n-4)=0. - R. J. Mathar, May 26 2025

PROG

(PARI) a(n) = prod(k=0, n-1, n+4*k+3);

(SageMath)