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 A385620 #13 Jul 05 2025 09:59:02
%S A385620 1,2,24,1064,158144,78427712,130391102464,725657074158592,
%T A385620 13450842239318679552,825492067428121929359360,
%U A385620 166724642619378284453845213184,110175812687250637947409895640473600,236918101449618886434191300434062010777600,1649425480856495624442166311045759714226010423296
%N A385620 E.g.f. A(x) satisfies A(x) = exp( x*(A(2*x) + A(3*x)) ).
%F A385620 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * (2^k+3^k) * binomial(n-1,k) * a(k) * a(n-1-k).
%t A385620 terms = 14; A[_] = 1; Do[A[x_] =Exp[x*(A[2*x] + A[3*x])]+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Jul 05 2025 *)
%o A385620 (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+3^j)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385620 Cf. A058014, A096538, A385526.
%K A385620 nonn
%O A385620 0,2
%A A385620 _Seiichi Manyama_, Jul 05 2025