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Cumulative product of triple factorial A007661.
0

%I #10 Jan 25 2024 14:28:40

%S 1,1,2,6,24,240,4320,120960,9676800,1567641600,438939648000,

%T 386266890240000,750902834626560000,2733286318040678400000,

%U 33674087438261157888000000,981936389699695364014080000000

%N Cumulative product of triple factorial A007661.

%C This is the product analog of what for sums is A114347.

%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!!!. a(n) = Product_{j=0..n} A007661(j). a(n) = n!!! * a(n-1) where a(0) = 1, a(1) = 1 and n >= 2. a(n) = n*(n-3)!!! * a(n-1) where a(0) = 1, a(1) = 1, a(2) = 2 and n >= 3.

%e a(10) = 1!!! * 2!!! * 3!!! * 4!!! * 5!!! * 6!!! * 7!!! * 8!!! * 9!!! * 10!!!

%e = 1 * 2 * 3 * 4 * 10 * 18 * 28 * 80 * 162 * 280 = 438939648000 = 2^15 * 3^7 * 5^3 * 7^2.

%Y Cf. A006882, A000178, A114347.

%K easy,nonn

%O 0,3

%A _Jonathan Vos Post_, Feb 18 2006