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 A180687 #6 Apr 04 2023 10:46:43
%S A180687 1,2,8,70,2008,209018,76000040,94978699326,410326957417208,
%T A180687 6211396910763188786,334321755307017208207432,
%U A180687 64835518006826024523658441206,45812575197824183928260946747286552
%N A180687 G.f.: A(x) = Sum_{n>=0} log(1 + 2^n*x/(1-x))^n/n!.
%F A180687 a(n) = Sum_{k=0..n} binomial(2^k, k) * binomial(n-1, n-k) for n >= 0. - _Paul D. Hanna_, Apr 04 2023
%e A180687 G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 70*x^4 + 2008*x^5 +...
%e A180687 A(x) = Sum_{n>=0} log(1 + 2^n*x + 2^n*x^2 + 2^n*x^3 + 2^n*x^4 +...)^n/n!.
%e A180687 A(x) = 1 + log(1+2x/(1-x)) + log(1+4x/(1-x))^2/2! + log(1+8x/(1-x))^3/3! +...
%o A180687 (PARI) {a(n)=polcoeff(sum(m=0, n, log(1+2^m*x/(1-x+x*O(x^n)))^m/m!), n)}
%Y A180687 Cf. variants: A159602, A060690.
%K A180687 nonn
%O A180687 0,2
%A A180687 _Paul D. Hanna_, Sep 16 2010