OFFSET
0,3
FORMULA
MAPLE
seq(n!*coeff(series(exp(-1+mul(1/(1-x^k)^k, k=1..100)), x=0, 20), x, n), n=0..19); # Paolo P. Lava, Jan 09 2019
MATHEMATICA
nmax = 19; CoefficientList[Series[Exp[-1 + Product[1/(1 - x^k)^k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[Exp[-1 + Exp[Sum[DivisorSigma[2, k] x^k/k, {k, 1, nmax}]]], {x, 0, nmax}], x] Range[0, nmax]!
p[n_] := p[n] = Sum[DivisorSigma[2, k] p[n - k], {k, n}]/n; p[0] = 1; a[n_] := a[n] = Sum[p[k] k! Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 19}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 29 2018
STATUS
approved