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 A385846 #10 Jul 10 2025 10:58:46
%S A385846 1,1,1,1,1,25,3025,1092025,918393025,1543818675025,4670051491951201,
%T A385846 23541729570926148241,186474039931306081488961,
%U A385846 2215498068423847604734793641,38020162352221648825602734209201,913434400512125113270449340963296649,29925024395177730837015182640209851847809
%N A385846 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x^5*A''''(x))).
%F A385846 a(n) = 1 + Sum_{k=0..n-1} (-6*k + 11*k^2 - 6*k^3 + k^4) * a(k) * a(n-1-k).
%t A385846 terms = 17; A[_] = 0; Do[A[x_] = 1/((1 - x) * (1 - x^5*A''''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 10 2025 *)
%o A385846 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, sum(k=1, 4, stirling(4, k, 1)*j^k)*v[j+1]*v[i-j])); v;
%Y A385846 Cf. A143917, A385844, A385845.
%Y A385846 Cf. A385760.
%K A385846 nonn
%O A385846 0,6
%A A385846 _Seiichi Manyama_, Jul 09 2025