A307568 Expansion of e.g.f. Product_{j>=1} (1 + (-1 + Product_{k>=1} (1 + x^k/k!))^j/j!).

1, 1, 2, 11, 53, 367, 2680, 22794, 216830, 2325825, 27553582, 351008143, 4810073427, 70013351163, 1082415831294, 17747223519590, 308327844386251, 5667992273930453, 109909795136025124, 2239594732588547820, 47747134765967675665, 1060822117856654685661, 24480836958809924299702

Offset

0,3

Links

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

Formula

E.g.f.: g(g(x) - 1), where g(x) = e.g.f. of A007837.

Mathematica

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

Crossrefs

Cf. A007837, A307567.

Sequence in context: A030281 A289847 A063767 * A161559 A291386 A128748

Adjacent sequences: A307565 A307566 A307567 * A307569 A307570 A307571

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 15 2019

Status

approved