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%I #4 Jul 11 2020 07:39:51
%S 2,7,39,314,3379,45440,733335,13807364,297105507,7192224540,
%T 193452015049,5723688147650,184742675924105,6459822765521016,
%U 243253254143586291,9814313764465482774,422366963490734937123,19312961877700115922410,935042624229107088382095
%N a(n) = prime(n) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * k * a(k) * prime(n-k).
%F E.g.f.: -log(1 - Sum_{k>=1} prime(k) * x^k / k!).
%t a[n_] := a[n] = Prime[n] + (1/n) Sum[Binomial[n, k] k a[k] Prime[n - k], {k, 1, n - 1}]; Table[a[n], {n, 1, 19}]
%t nmax = 19; CoefficientList[Series[-Log[1 - Sum[Prime[k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! // Rest
%Y Cf. A000040, A007446, A007447, A307770.
%K nonn
%O 1,1
%A _Ilya Gutkovskiy_, Jul 10 2020
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