This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358032 #14 Oct 26 2022 12:52:45 %S A358032 1,2,4,16,66,438,2694,25296,204576,2509728,24912816,381010320, %T A358032 4440815472,82150191264,1089159690912,23879423005440,351430312958208, %U A358032 9005004020293632,144184020764472576,4277182103330660352,73227226213747521792,2499666592623881921280 %N A358032 Expansion of e.g.f. (1 + log(1+x))/(1 - log(1+x) * (1 + log(1+x))). %F A358032 a(n) = Sum_{k=0..n} k! * Fibonacci(k+2) * Stirling1(n,k). %F A358032 a(n) = A005444(n) + A005445(n). %o A358032 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1+log(1+x))/(1-log(1+x)*(1+log(1+x))))) %o A358032 (PARI) a(n) = sum(k=0, n, k!*fibonacci(k+2)*stirling(n, k, 1)); %Y A358032 Cf. A005444, A005445. %Y A358032 Cf. A000557, A358031. %K A358032 nonn %O A358032 0,2 %A A358032 _Seiichi Manyama_, Oct 25 2022