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%I #4 Sep 20 2021 08:51:42
%S 1,0,1,2,6,64,170,2988,14616,180192,1934712,21673200,300266736,
%T 4220710272,61785461712,1003589762784,17448621367680,327598207658496,
%U 6279739240655232,134169095009652480,2817563310900129024,64570676279407718400,1547773850801172960000,38824156236466815920640
%N E.g.f.: 1 / (1 - Sum_{k>=1} x^prime(k) / prime(k)).
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * A010051(k) * a(n-k).
%t nmax = 23; CoefficientList[Series[1/(1 - Sum[x^Prime[k]/Prime[k], {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (k - 1)! Boole[PrimeQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]
%Y Cf. A007840, A010051, A023360, A218002, A347948.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Sep 20 2021
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