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A376400 a(0) = 1, and for n > 0, a(n) = a(n-1) * A276076(a(n-1)), where A276076 is the factorial base exp-function.

%I A376400 #19 Nov 04 2024 12:33:08
%S A376400 1,2,6,30,1050,70814493750,
%T A376400 7568077812763134673885891483463343434987134201379042046671543939118568739667281250
%N A376400 a(0) = 1, and for n > 0, a(n) = a(n-1) * A276076(a(n-1)), where A276076 is the factorial base exp-function.
%C A376400 a(7) has 2129 (decimal) digits.
%C A376400 Like A376399, this satisfies A276075(a(n)) = a(n-1) + A276075(a(n-1)), for all n >= 1, so also here, applying A276075 to the terms gives the partial sums shifted right once, A376401.
%C A376400 However, unlike A376399, this is not a subsequence of A276078: a(5) = 70814493750 is the first term that is in A276079.
%H A376400 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%o A376400 (PARI)
%o A376400 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 A376400 A376400(n) = if(!n,1,my(x=A376400(n-1)); x*A276076(x));
%Y A376400 Cf. A276075, A276076, A276078, A276079, A376399, A376403.
%Y A376400 Cf. A376401 (= A276075(a(n)), also gives the partial sums from its second term onward).
%Y A376400 Cf. also analogous sequences A002110 (for A276086) and A376408 (for A019565).
%K A376400 nonn
%O A376400 0,2
%A A376400 _Antti Karttunen_, Nov 02 2024