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 A353951 #5 May 13 2022 10:00:40
%S A353951 1,1,1,1,1,1,-1,-2,-3,-2,4,-1,5,2,-4,-8,-9,-3,-3,12,19,-6,6,-38,-27,
%T A353951 -32,13,56,50,99,-49,-135,-162,-258,83,114,468,359,-40,-390,-1215,
%U A353951 -791,-526,876,2640,1816,1673,-3404,-4516,-6527,-3640,5320,9282,18019,7210
%N A353951 Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + x + Sum_{n>=2} prime(n-1)*x^n.
%t A353951 A[m_, n_] := A[m, n] = Which[m == 1, If[n == 1, 1, Prime[n - 1]], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 55]
%Y A353951 Cf. A008578, A147557, A305882, A353605, A353606, A353950.
%K A353951 sign
%O A353951 1,8
%A A353951 _Ilya Gutkovskiy_, May 12 2022