login
a(n) = Abs(StirlingS1(4*n,n)).
2

%I #7 Jan 06 2016 17:19:16

%S 1,6,13068,150917976,5056995703824,371384787345228000,

%T 50779532534302850198976,11616723683566425573507775872,

%U 4123257155075936045020928754053376,2146734309994687055429549444238169536000,1569808063009967047226374755685187772671339520

%N a(n) = Abs(StirlingS1(4*n,n)).

%C Generally, for p>=2 is Abs(StirlingS1(p*n,n)) asymptotic to n^((p-1)*n) * c^(p*n) * p^((2*p-1)*n) / (sqrt(2*Pi*p*(c-1)*n) * exp((p-1)*n) * (c*p-1)^((p-1)*n)), where c = -LambertW(-1,-exp(-1/p)/p).

%F a(n) ~ n^(3*n) * c^(4*n) * 2^(14*n-1) / (sqrt(2*Pi*(c-1)*n) * exp(3*n) * (4*c-1)^(3*n)), where c = -LambertW(-1,-exp(-1/4)/4) = 2.58666298226305388118285...

%p seq(abs(Stirling1(4*n,n)), n=0..20);

%t Table[Abs[StirlingS1[4*n, n]],{n,0,20}]

%Y Cf. A187646, A237993, A217914.

%K nonn,easy

%O 0,2

%A _Vaclav Kotesovec_, May 20 2014