A336185 a(n) = prime(n) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * k * a(k) * prime(n-k).
2, 7, 39, 314, 3379, 45440, 733335, 13807364, 297105507, 7192224540, 193452015049, 5723688147650, 184742675924105, 6459822765521016, 243253254143586291, 9814313764465482774, 422366963490734937123, 19312961877700115922410, 935042624229107088382095
Offset: 1
Keywords
Programs
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Mathematica
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}] nmax = 19; CoefficientList[Series[-Log[1 - Sum[Prime[k] x^k/k!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Formula
E.g.f.: -log(1 - Sum_{k>=1} prime(k) * x^k / k!).