A368267 Expansion of e.g.f. exp(2*x) / (1 - 2*x*exp(x)).
1, 4, 24, 206, 2344, 33322, 568420, 11312366, 257293872, 6583516946, 187173328444, 5853594770806, 199705444781512, 7381068971010074, 293787494031046740, 12528831526596461438, 569923490454177217120, 27545552296682691393058
Offset: 0
Programs
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PARI
a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k+2)^k/k!);
Formula
a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k+2)^k / k!.
a(n) ~ n! / (4 * LambertW(1/2)^(n+2) * (LambertW(1/2) + 1)). - Vaclav Kotesovec, Dec 29 2023