This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108895 #17 Dec 18 2019 02:02:46
%S A108895 1,2,4,7,11,16,28,49,81,126,246,477,861,1446,3126,6591,12735,22680,
%T A108895 52920,118755,241635,450480,1115760,2629965,5579085,10800210,28097490,
%U A108895 68981025,151556385,302969010,821887410,2089276995,4731688515
%N A108895 Partial sums of quadruple factorial numbers n!!!! (A007662).
%C A108895 Quadruple factorial numbers n!!!! = n*(n-4)!!!!, 0!!!! = 1!!!! = 1, 2!!!! = 2, 3!!!! = 3. The cumulative sum a(n) is prime for n = 1, 3, 4 and never again, as all values from a(8) = 81 are multiples of 3. The cumulative sum a(n) is semiprime for n = 2, 7 and never again, as all values from a(16) are divisible by both 3 and 5.
%D A108895 J. Spanier and K. B. Oldham, An Atlas of Functions, Hemisphere, NY, 1987, p. 23.
%F A108895 a(n) = Sum_{i=0..n} i!!!!.
%F A108895 a(n) = Sum_{i=0..n} A007662(i).
%e A108895 a(31) = 1 + 1 + 2 + 3 + 4 + 5 + 12 + 21 + 32 + 45 + 120 + 231 + 384 + 585 + 1680 + 3465 + 6144 + 9945 + 30240 + 65835 + 122880 + 208845 + 665280 + 1514205 + 2949120 + 5221125 + 17297280 + 40883535 + 82575360 + 151412625 + 518918400 + 1267389585 = 2089276995 = 3 * 5 * 13 * 337 * 31793.
%t A108895 NFactorialM[n_Integer, m_Integer] := Block[{k = n, p = Max[1, n]}, While[k > m, k -= m; p *= k]; p]; Table[ Sum[ NFactorialM[i, 4], {i, 0, n}], {n, 0, 33}] (* _Robert G. Wilson v_, Feb 21 2006 *)
%Y A108895 Cf. A000040, A001358, A007662, A114347.
%K A108895 easy,nonn
%O A108895 0,2
%A A108895 _Jonathan Vos Post_, Feb 08 2006