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 A307899 #5 May 04 2019 21:51:54
%S A307899 1,0,-2,-3,-1,5,10,9,-4,-26,-43,-33,35,148,219,98,-316,-857,-983,23,
%T A307899 2296,4501,3712,-2906,-14257,-21771,-10811,28282,81209,97292,7960,
%U A307899 -207185,-431595,-386033,219344,1322141,2134126,1226554,-2443765,-7684081,-9726127,-1791806,18712361,41428590,39753658
%N A307899 Expansion of 1/(1 + x * Sum_{k>=1} prime(k)*x^k).
%C A307899 Alternating antidiagonal sums of square array, in which row m equals the m-fold convolution of primes with themselves.
%F A307899 Recurrence: a(n+1) = -Sum_{k=1..n} prime(k)*a(n-k).
%t A307899 nmax = 44; CoefficientList[Series[1/(1 + x Sum[Prime[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%t A307899 a[0] = 1; a[n_] := a[n] = -Sum[Prime[k] a[n - k - 1], {k, 1, n - 1}]; Table[a[n], {n, 0, 44}]
%Y A307899 Cf. A000040, A030017, A030018, A307898.
%K A307899 sign
%O A307899 0,3
%A A307899 _Ilya Gutkovskiy_, May 04 2019