OFFSET
0,3
FORMULA
G.f.: Sum_{j>=0} j!*Bell(j)*x^j / Product_{k=1..j} (1 - k*x).
a(n) = Sum_{k=0..n} Stirling2(n,k)*k!*Bell(k).
MATHEMATICA
nmax = 18; CoefficientList[Series[Sum[(Exp[x] - 1)^j/Product[(1 - k (Exp[x] - 1)), {k, 1, j}], {j, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 18; CoefficientList[Series[Sum[j! BellB[j] x^j/Product[(1 - k x), {k, 1, j}], {j, 0, nmax}], {x, 0, nmax}], x]
Table[Sum[StirlingS2[n, k] k! BellB[k], {k, 0, n}], {n, 0, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 05 2019
STATUS
approved