OFFSET
0,3
FORMULA
E.g.f.: exp(-Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*((j - 1)!)^k)).
MAPLE
seq(n!*coeff(series(mul((1 - x^k/(k - 1)!), k=1..100), x=0, 25), x, n), n=0..24); # Paolo P. Lava, Jan 09 2019
MATHEMATICA
nmax = 24; CoefficientList[Series[Product[(1 - x^k/(k - 1)!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[Exp[-Sum[Sum[x^(j k)/(k (j - 1)!^k), {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[Sum[-d (d - 1)!^(-k/d), {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 24}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Sep 13 2018
STATUS
approved