A308338 Expansion of e.g.f. exp(-1 + Product_{k>=1} (1 + x^k/k)).
1, 1, 2, 9, 44, 270, 2064, 17682, 171296, 1867968, 22470840, 294493320, 4195969392, 64416698112, 1059685905264, 18609306423120, 347179119075840, 6855335163907200, 142889687354283264, 3133647091691585280, 72124075333003155840, 1738384773846440146560
Offset: 0
Keywords
Programs
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Mathematica
nmax = 21; CoefficientList[Series[Exp[Product[(1 + x^k/k), {k, 1, nmax}] - 1], {x, 0, nmax}], x] Range[0, nmax]!
Formula
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1)*A007838(k)*a(n-k).