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 A353160 #8 Apr 28 2022 09:45:55
%S A353160 3,2,0,4,-4,6,-8,11,0,-18,40,-67,88,-78,-4,205,-524,926,-1234,1060,
%T A353160 140,-2998,7900,-14132,18858,-16280,-2710,48783,-127826,228784,
%U A353160 -306494,263582,55144,-829538,2160120,-3864533,5172792,-4406277,-1118324,14531101,-37606792
%N A353160 Product_{n>=1} (1 + x^n)^a(n) = 1 + Sum_{n>=1} prime(n+1) * x^n.
%C A353160 Inverse weigh transform of odd primes.
%p A353160 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A353160 add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
%p A353160 end:
%p A353160 a:= proc(n) option remember; ithprime(n+1)-b(n, n-1) end:
%p A353160 seq(a(n), n=1..50); # _Alois P. Heinz_, Apr 28 2022
%t A353160 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] = Prime[n + 1] - b[n, n - 1]; Table[a[n], {n, 1, 41}]
%Y A353160 Cf. A006005, A065091, A305871, A352609, A353161.
%K A353160 sign
%O A353160 1,1
%A A353160 _Ilya Gutkovskiy_, Apr 28 2022