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 A307898 #6 May 04 2019 21:51:48
%S A307898 1,0,2,3,9,19,48,107,258,594,1405,3277,7693,18004,42203,98834,231592,
%T A307898 542497,1271003,2977529,6975674,16342011,38285178,89691782,210124363,
%U A307898 492265243,1153247379,2701752062,6329489153,14828313076,34738805240,81383803849,190660665579,446667359857,1046423138962
%N A307898 Expansion of 1/(1 - x * Sum_{k>=1} prime(k)*x^k).
%C A307898 Antidiagonal sums of square array, in which row m equals the m-fold convolution of primes with themselves.
%F A307898 Recurrence: a(n+1) = Sum_{k=1..n} prime(k)*a(n-k).
%t A307898 nmax = 34; CoefficientList[Series[1/(1 - x Sum[Prime[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%t A307898 a[0] = 1; a[n_] := a[n] = Sum[Prime[k] a[n - k - 1], {k, 1, n - 1}]; Table[a[n], {n, 0, 34}]
%Y A307898 Cf. A000040, A030017, A030018, A300662, A307899.
%K A307898 nonn
%O A307898 0,3
%A A307898 _Ilya Gutkovskiy_, May 04 2019