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

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1)*A007838(k)*a(n-k).

Mathematica

nmax = 21; CoefficientList[Series[Exp[Product[(1 + x^k/k), {k, 1, nmax}] - 1], {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A007838, A308336, A308337.

Sequence in context: A182386 A000166 A093464 * A196301 A347571 A331559

Adjacent sequences: A308335 A308336 A308337 * A308339 A308340 A308341

Keyword

nonn

Author

Ilya Gutkovskiy, May 20 2019

Status

approved