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 A385546 #14 Jul 03 2025 07:29:26
%S A385546 1,1,5,73,2841,275841,64191133,34819498953,43138054887665,
%T A385546 120180168811524673,743714973197251893621,10121932780068673030506249,
%U A385546 300492979488426431579059718281,19324971141736799892467667226925889,2676450415125002650227336306537165370253,794234262095484293816451881720629809901365001
%N A385546 E.g.f. A(x) satisfies A(x) = Sum_{k>=0} x^k/k! * A(2*k*x).
%F A385546 a(0) = 1; a(n) = Sum_{k=0..n-1} (2*(n-k))^k * binomial(n,k) * a(k).
%F A385546 a(n) ~ c * n! * (1 + sqrt(2))^n * 2^(n*(n-3)/2), where c = 0.890249679316305512447698257069341300111198385329042058845194612667048446402873... - _Vaclav Kotesovec_, Jul 03 2025
%t A385546 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n,k] * 2^k * (n-k)^k * a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 03 2025 *)
%o A385546 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (2*(i-j))^j*binomial(i, j)*v[j+1])); v;
%Y A385546 Cf. A125281, A385550.
%Y A385546 Cf. A195067.
%K A385546 nonn
%O A385546 0,3
%A A385546 _Seiichi Manyama_, Jul 03 2025