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%I #14 Oct 26 2022 12:52:45
%S 1,2,4,16,66,438,2694,25296,204576,2509728,24912816,381010320,
%T 4440815472,82150191264,1089159690912,23879423005440,351430312958208,
%U 9005004020293632,144184020764472576,4277182103330660352,73227226213747521792,2499666592623881921280
%N Expansion of e.g.f. (1 + log(1+x))/(1 - log(1+x) * (1 + log(1+x))).
%F a(n) = Sum_{k=0..n} k! * Fibonacci(k+2) * Stirling1(n,k).
%F a(n) = A005444(n) + A005445(n).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1+log(1+x))/(1-log(1+x)*(1+log(1+x)))))
%o (PARI) a(n) = sum(k=0, n, k!*fibonacci(k+2)*stirling(n, k, 1));
%Y Cf. A005444, A005445.
%Y Cf. A000557, A358031.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 25 2022
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