A242019 - OEIS

%I #9 Aug 11 2014 10:52:37

%S 1,1,33,3409,728575,265362370,147228369351,115651594418010,

%T 122167455441632423,167035663137431205196,287018982366654934570328,

%U 605456750773492887086145669,1538306721887736189212800143193,4633572348321634923252339927247392

%N a(n) = Sum_{k=0..n} Stirling2(2*n+k, k) * C(n, k).

%F a(n) ~ c * (r^4/((1-r)*(2*r-1)^2))^n * n^(2*n-1/2) / exp(2*n), where r = 0.949867370961706500554205072094811326960829788646... is the root of the equation (1-r)*(2+r)/r^2 = -LambertW(-exp(-1-2/r)*(2+r)/r), and c = 0.42307980713011095154197903821771057626302758607...

%t Table[Sum[Binomial[n,k] * StirlingS2[2*n+k,k],{k,0,n}],{n,0,20}]

%Y Cf. A243942, A218667.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Aug 11 2014