OFFSET
0,3
FORMULA
E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} log(1/(1 - x))^(j*k)/(k*(j!)^k)).
a(n) = Sum_{k=0..n} |Stirling1(n,k)|*A005651(k).
a(n) ~ c * sqrt(2*Pi) * n^(n + 1/2) / (exp(1) - 1)^(n+1), where c = A247551 = Product_{k>=2} 1/(1-1/k!). - Vaclav Kotesovec, Apr 13 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1/(1 - Log[1/(1 - x)]^k/k!), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Sum[Sum[Log[1/(1 - x)]^(j k)/(k (j!)^k), {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] Total[Apply[Multinomial, IntegerPartitions[k], {1}]], {k, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 12 2019
STATUS
approved