%I #8 Jan 25 2024 14:30:20

%S 1,1,2,6,24,120,1440,30240,967680,43545600,5225472000,1207084032000,

%T 463520268288000,271159356948480000,455547719673446400000,

%U 1578472848668491776000000,9698137182219213471744000000

%N Cumulative product of quadruple factorial A007662.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Multifactorial.html">Multifactorial.</a>

%F a(n) = Product_{j=0..n} j!!!!.

%F a(n) = Product_{j=0..n} A007662(j).

%F a(n) = n!!!! * a(n-1) where a(0) = 1, a(1) = 1 and n >= 2.

%F a(n) = n*(n-4)!!!! * a(n-1) where a(0) = 1, a(1) = 1, a(2) = 2.

%e a(10) = 1!!!! * 2!!!! * 3!!!! * 4!!!! * 5!!!! * 6!!!! * 7!!!! * 8!!!! * 9!!!! * 10!!!! = 1 * 2 * 3 * 4 * 5 * 12 * 21 * 32 * 45 * 120 = 5225472000 = 2^13 * 3^6 * 5^3 * 7.

%Y Cf. A006882, A007662, A000178, A114347.

%K easy,nonn

%O 0,3

%A _Jonathan Vos Post_, Feb 18 2006