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.

0, 1, 3, 9, 39, 1089, 520179, 1466909163669354042297

Offset: 0

Author

Antti Karttunen, Nov 02 2024

Keywords

• nonn

Comments

a(8) has 212 digits, a(9) has 10654 digits.

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A276075, A276076, A376399, A376401.

Cf. also A143293 (when prepended with 0, an analogous sequence for A276086).

Programs

PARI

A276076(n) = { my(m=1, p=2, i=2); while(n, m *= (p^(n%i)); n = n\i; p = nextprime(1+p); i++); (m); };
A376403(n) = if(!n,0,A376403(n-1)+A276076(A376403(n-1)));

Formula

a(n) = A276075(A376399(n)).

a(0) = 0; and for n > 0, a(n) = a(n-1) + A376399(n-1) = Sum_{i=0..n-1} A376399(i).