A360471 - OEIS

%I #23 Feb 17 2023 15:48:14

%S 0,1,6,75,1476,39805,1366278,56998179,2800588808,158420939193,

%T 10140538486410,724652822705119,57187947315670284,4939834587311520117,

%U 463572330418586227790,46965096302630022564315,5108915146530700018466832,593925863391217441843199089

%N E.g.f. satisfies A(x) = x * exp( 2*A(x) + x * exp(2*A(x)) ).

%H Seiichi Manyama, <a href="/A360471/b360471.txt">Table of n, a(n) for n = 0..337</a>

%F a(n) = Sum_{k=1..n} k^(n-k) * (2*n)^(k-1) * binomial(n,k).

%F a(n) ~ 2^(n - 1/2) * s^n * n^(n-1) / (sqrt(2 + 1/s - 4*s) * (1 - 2*s)^n * exp(n*(1 - 2*s))), where s = 0.3875920123187127910093095185777835252050660050582... is the root of the equation 2*s*(1 + LambertW(s)) = 1. - _Vaclav Kotesovec_, Feb 17 2023

%o (PARI) a(n) = sum(k=1, n, k^(n-k)*(2*n)^(k-1)*binomial(n, k));

%Y Cf. A055779, A360442, A360474, A360481.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 09 2023