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%I #20 Mar 01 2022 01:36:09
%S 1,0,1,1,9,11,295,337,13041,45550,1043211,3359786,150500053,440947300,
%T 23238057921,145733451241,5097210717873,29028404123105,
%U 1710073810205317,8663532297784519,574604164708374861,5108822296820280256,246335435270285805885
%N Expansion of e.g.f. Product_{k>=1} 1/(1 - x^prime(k))^(1/prime(k)!).
%F E.g.f.: exp( Sum_{k>=1} A352012(k)*x^k/k! ) where A352012(k) = Sum_{p|k, p prime} (k-1)!/(p-1)!.
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^(isprime(k)/k!))))
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, isprime(d)*(k-1)!/(d-1)!)*x^k/k!))))
%Y Cf. A209902, A318913, A352012.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Feb 28 2022