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