A384256 - OEIS

A384256

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

1, 2, 18, 280, 6160, 174960, 6086080, 250490240, 11904278400, 641472832000, 38645634227200, 2573895458534400, 187787322731008000, 14894027431162880000, 1275931456704672768000, 117412145664335441920000, 11550258696757088788480000, 1209613643310990696210432000

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OFFSET

0,2

LINKS

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

FORMULA

a(n) = 3^n * RisingFactorial((n+1)/3,n).

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

PROG

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

(SageMath)

def a(n): return 3^n*rising_factorial((n+1)/3, n)