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 A380639 #11 Jan 29 2025 08:10:38
%S A380639 1,1,9,97,1297,20961,398041,8678209,213337377,5830560577,175187949481,
%T A380639 5734893998241,203021979225649,7724154592735777,314158263983430777,
%U A380639 13597375157683820161,623802598335834369601,30228101725367033318529,1542430410234859308052297
%N A380639 Expansion of e.g.f. exp(x/(1 - 2*x)^2).
%F A380639 a(n) = n! * Sum_{k=0..n} 2^k * binomial(2*n-k-1,k)/(n-k)!.
%F A380639 E.g.f.: exp( Sum_{k>=1} k * 2^(k-1) * x^k ).
%F A380639 a(n) ~ 2^n * n^(n - 1/6) / (sqrt(3) * exp(n - 3*n^(2/3)/2 + 1/24)). - _Vaclav Kotesovec_, Jan 29 2025
%o A380639 (PARI) a(n) = n!*sum(k=0, n, 2^k*binomial(2*n-k-1, k)/(n-k)!);
%Y A380639 Cf. A380636, A380640.
%Y A380639 Cf. A082579.
%K A380639 nonn,easy
%O A380639 0,3
%A A380639 _Seiichi Manyama_, Jan 28 2025