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

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1)*A007837(k)*a(n-k).

Mathematica

nmax = 22; CoefficientList[Series[Exp[Product[(1 + x^k/k!), {k, 1, nmax}] - 1], {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A007837, A143463, A182927, A308338.

Sequence in context: A150826 A150827 A150828 * A120774 A261052 A128324

Adjacent sequences: A308333 A308334 A308335 * A308337 A308338 A308339

Keyword

nonn

Author

Ilya Gutkovskiy, May 20 2019

Status

approved