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 A353161 #7 Apr 28 2022 10:05:26
%S A353161 1,2,1,3,1,2,-1,1,-3,-1,4,1,5,2,-4,-4,-9,0,-3,14,19,4,6,-38,-27,-17,5,
%T A353161 59,50,103,-49,-100,-142,-222,83,138,468,362,0,-313,-1215,-599,-526,
%U A353161 961,2572,1837,1673,-2858,-4516,-6182,-3880,5981,9282,18218,7414,-8554,-24446
%N A353161 Product_{n>=1} (1 + x^n)^a(n) = 1 + x + Sum_{n>=2} prime(n-1) * x^n.
%C A353161 Inverse weigh transform of {1, primes}.
%p A353161 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A353161 add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
%p A353161 end:
%p A353161 a:= proc(n) option remember; `if`(n=1, 1, ithprime(n-1))-b(n, n-1) end:
%p A353161 seq(a(n), n=1..60); # _Alois P. Heinz_, Apr 28 2022
%t A353161 p[n_] := If[n == 1, 1, Prime[n - 1]]; b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; a[n_] := a[n] = p[n] - b[n, n - 1]; Table[a[n], {n, 1, 57}]
%Y A353161 Cf. A008578, A030011, A305871, A353160.
%K A353161 sign
%O A353161 1,2
%A A353161 _Ilya Gutkovskiy_, Apr 28 2022