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 A376403 #19 Nov 04 2024 12:33:21
%S A376403 0,1,3,9,39,1089,520179,1466909163669354042297
%N A376403 a(0) = 0, and for n > 0, a(n) = a(n-1) + A276076(a(n-1)), where A276076 is the factorial base exp-function.
%C A376403 a(8) has 212 digits, a(9) has 10654 digits.
%C A376403 By induction, it is easy to see that formula a(n) = A276075(A376399(n)) implies that from the second term onward, this sequence gives the partial sums of A376399. See more comments in that sequence.
%H A376403 Antti Karttunen, <a href="/A376403/b376403.txt">Table of n, a(n) for n = 0..8</a>
%H A376403 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A376403 a(n) = A276075(A376399(n)).
%F A376403 a(0) = 0; and for n > 0, a(n) = a(n-1) + A376399(n-1) = Sum_{i=0..n-1} A376399(i).
%o A376403 (PARI)
%o A376403 A276076(n) = { my(m=1, p=2, i=2); while(n, m *= (p^(n%i)); n = n\i; p = nextprime(1+p); i++); (m); };
%o A376403 A376403(n) = if(!n,0,A376403(n-1)+A276076(A376403(n-1)));
%Y A376403 Cf. A276075, A276076, A376399, A376401.
%Y A376403 Cf. also A143293 (when prepended with 0, an analogous sequence for A276086).
%K A376403 nonn
%O A376403 0,3
%A A376403 _Antti Karttunen_, Nov 02 2024