A332024 E.g.f.: Product_{k>=1} (1 + x^k/(k!*(1 - x)^k)).

1, 1, 3, 16, 113, 956, 9382, 105253, 1334517, 18904936, 295787126, 5056826039, 93594929738, 1861321879535, 39536014577711, 892763601542509, 21352130132268541, 539243894127067888, 14342761454293102006, 400830115867761118963, 11743833994363640228070

Offset: 0

Author

Ilya Gutkovskiy, Feb 13 2020

Keywords

• nonn

Crossrefs

Cf. A007837, A084357, A129519, A320567, A330649.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 + x^k/(k! (1 - x)^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

PARI

seq(n)={Vec(serlaplace(prod(k=1, n, (1 + x^k/(k!*(1 - x)^k)) + O(x*x^n))))} \\ Andrew Howroyd, Feb 13 2020

Formula

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