A242019 a(n) = Sum_{k=0..n} Stirling2(2*n+k, k) * C(n, k).

1, 1, 33, 3409, 728575, 265362370, 147228369351, 115651594418010, 122167455441632423, 167035663137431205196, 287018982366654934570328, 605456750773492887086145669, 1538306721887736189212800143193, 4633572348321634923252339927247392

Offset: 0

Author

Vaclav Kotesovec, Aug 11 2014

Keywords

• nonn

Crossrefs

Cf. A243942, A218667.

Programs

Mathematica

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

Formula

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...