OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..390
FORMULA
a(n) = Sum_{k=0..n} |Stirling1(n,k)| * (2*k-1)!!.
a(n) ~ n^n / (exp(n/2) * (exp(1/2) - 1)^(n + 1/2)). - Vaclav Kotesovec, Aug 09 2021
a(0) = 1; a(n) = Sum_{k=1..n} (2 - k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 09 2023
MATHEMATICA
nmax = 19; CoefficientList[Series[1/Sqrt[1 + 2 Log[1 - x]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] (2 k - 1)!!, {k, 0, n}], {n, 0, 19}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 09 2021
STATUS
approved