%I #11 Dec 29 2023 06:03:55
%S 1,4,24,206,2344,33322,568420,11312366,257293872,6583516946,
%T 187173328444,5853594770806,199705444781512,7381068971010074,
%U 293787494031046740,12528831526596461438,569923490454177217120,27545552296682691393058
%N Expansion of e.g.f. exp(2*x) / (1 - 2*x*exp(x)).
%F a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k+2)^k / k!.
%F a(n) ~ n! / (4 * LambertW(1/2)^(n+2) * (LambertW(1/2) + 1)). - _Vaclav Kotesovec_, Dec 29 2023
%o (PARI) a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k+2)^k/k!);
%Y Cf. A351762, A368236, A368268, A368269.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Dec 19 2023
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