%I #12 Mar 31 2023 10:06:51
%S 1,2,4,7,11,21,39,67,147,309,589,1469,3413,7053,19373,48533,106773,
%T 316213,841093,1947653,6136453,17158933,41503253,137845653,402385173,
%U 1010993173,3515895573,10658462613,27699486613,100341656213,314618667413,842890411413
%N Cumulative sum of triple factorial numbers a(n) = n!!! (A007661).
%C Triple factorial numbers n!!! = n*(n-3)!!!, 0!!! = 1!!! = 1, 2!!! = 2.
%C The cumulative sum a(n) is prime for n = 1, 3, 4, 7, 12, 14, 15, 17, 19.
%C The cumulative sum a(n) is semiprime for n = 2, 5, 6, 9, 10, 11, 13, 16, 18, 20, 22, 26, 28, 29.
%D J. Spanier and K. B. Oldham, An Atlas of Functions, Hemisphere, NY, 1987, p. 23.
%H Delbert L. Johnson, <a href="/A114347/b114347.txt">Table of n, a(n) for n = 0..1141</a>
%F a(n) = Sum_{i=0..n} i!!!.
%F a(n) = Sum_{i=0..n} A007661(i).
%e a(29) = 1 + 1 + 2 + 3 + 4 + 10 + 18 + 28 + 80 + 162 + 280 + 880 + 1944 + 3640 + 12320 + 29160 + 58240 + 209440 + 524880 + 1106560 + 4188800 + 11022480 + 24344320 + 96342400 + 264539520 + 608608000 + 2504902400 + 7142567040 + 17041024000 + 726421696 = 100341656213 = 79 * 1270147547.
%Y Cf. A000040, A001358, A007661.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Feb 08 2006