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A332024
E.g.f.: Product_{k>=1} (1 + x^k/(k!*(1 - x)^k)).
1
1, 1, 3, 16, 113, 956, 9382, 105253, 1334517, 18904936, 295787126, 5056826039, 93594929738, 1861321879535, 39536014577711, 892763601542509, 21352130132268541, 539243894127067888, 14342761454293102006, 400830115867761118963, 11743833994363640228070
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} binomial(n-1,k-1) * A007837(k) * n! / k!.
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1 + x^k/(k! (1 - x)^k)), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 13 2020
STATUS
approved