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%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