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 A383171 #11 Apr 18 2025 10:22:17
%S A383171 0,0,1,9,91,1090,15298,247352,4537132,93195696,2120623984,52973194560,
%T A383171 1441635171040,42464913775232,1346297567292416,45715740985471744,
%U A383171 1655552663185480448,63698261991541393408,2595107348458704209920,111613055867327344582656
%N A383171 Expansion of e.g.f. log(1 + log(1 - 2*x)/2)^2 / 2.
%F A383171 a(n) = Sum_{k=2..n} 2^(n-k) * |Stirling1(n,k) * Stirling1(k,2)|.
%F A383171 a(n) ~ sqrt(Pi) * log(n) * 2^(n + 1/2) * n^(n - 1/2) / (exp(1) - exp(-1))^n * (1 + (gamma + log(2) - log(exp(2)-1))/log(n)), where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Apr 18 2025
%o A383171 (PARI) a(n) = sum(k=2, n, 2^(n-k)*abs(stirling(n, k, 1)*stirling(k, 2, 1)));
%Y A383171 Cf. A383170, A383172.
%Y A383171 Cf. A341587, A383163.
%K A383171 nonn
%O A383171 0,4
%A A383171 _Seiichi Manyama_, Apr 18 2025