A308336 Expansion of e.g.f. exp(-1 + Product_{k>=1} (1 + x^k/k!)).
1, 1, 2, 8, 31, 147, 884, 5567, 39176, 311400, 2644490, 24206327, 239684768, 2519262527, 28077597357, 331892965533, 4130002336563, 53944450834303, 738940309779760, 10577568411051305, 157846971489443335, 2452481386778640564, 39589449956634478543
Offset: 0
Keywords
Programs
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Mathematica
nmax = 22; 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)*A007837(k)*a(n-k).