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 A385619 #11 Jul 05 2025 09:29:23
%S A385619 1,2,16,320,14176,1363872,288285760,135499302976,142083696478720,
%T A385619 331241746024775168,1705949708332396248064,19272264281263882812337152,
%U A385619 474329882865823082358501265408,25275628582523724268037232839274496,2899873213836728319564120809900380069888
%N A385619 E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(2*x)) ).
%F A385619 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * (2^k+1) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A385619 a(n) ~ c * n! * 2^(n*(n-1)/2), where c = 13.440025845363170742648943305743503903268661246000630477... - _Vaclav Kotesovec_, Jul 05 2025
%t A385619 terms = 15; A[_] = 1; Do[A[x_] =Exp[x*(A[x] + A[2*x])]+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Jul 05 2025 *)
%o A385619 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (j+1)*(2^j+1)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385619 Cf. A385617.
%K A385619 nonn
%O A385619 0,2
%A A385619 _Seiichi Manyama_, Jul 05 2025