%I #10 Dec 25 2023 10:01:54
%S 1,3,17,155,1937,30499,577793,12784155,323427041,9207390211,
%T 291277318065,10136705490779,384848820035057,15829002092015267,
%U 701141988610115617,33275461169171553371,1684504951149122303169,90604594879948059236099
%N Expansion of e.g.f. exp(x) / (1 + log(1 - 2*x)).
%F a(n) = 1 + Sum_{k=1..n} 2^k * (k-1)! * binomial(n,k) * a(n-k).
%F a(n) ~ sqrt(Pi) * exp(1/2 - exp(-1)/2) * 2^(n + 1/2) * n^(n + 1/2) / (exp(1) - 1)^(n+1). - _Vaclav Kotesovec_, Dec 25 2023
%o (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=1, i, 2^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;
%Y Cf. A291979, A368445.
%Y Cf. A343707, A368283.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Dec 24 2023