OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = Sum_{k=1..n} (Sum_{i=0..(n-k)} ((i+k-1)!*C(k+2*i-1,i+k-1) *stirling1(n, i+k))))/(k-1)!), n>0, a(0)=1.
a(n) ~ n^(n-1) / (sqrt(2)*exp(n-3/8)*(exp(1/4)-1)^(n-1/2)). - Vaclav Kotesovec, Jun 02 2013
MATHEMATICA
CoefficientList[Series[Exp[(1-Sqrt[1-4*Log[1+x]])/2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)
PROG
(Maxima) a(n):=if n=0 then 1 else sum((sum(((i+k-1)!*binomial(k+2*i-1, i+k-1) *stirling1(n, i+k)), i, 0, n-k))/(k-1)!, k, 1, n);
(PARI) x='x+O('x^50); Vec(serlaplace(exp((1-sqrt(1-4*log(1+x)))/2))) \\ G. C. Greubel, Jun 02 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Nov 22 2011
STATUS
approved