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 A195067 #15 Jul 03 2025 07:16:05
%S A195067 1,1,3,17,191,4261,189123,16723689,2949213319,1037964817357,
%T A195067 729449200732395,1024041038817726353,2872628913886690237679,
%U A195067 16105674069113302453209781,180504701103754829110217971731,4044484405239396750189431682523833
%N A195067 G.f. A(x) satisfies A(x) = Sum{n>=0} x^n * A(2*n*x).
%F A195067 a(n) = Sum_{k=0..n-1} 2^k*(n-k)^k * a(k) for n>0 with a(0)=1.
%F A195067 a(n) ~ c * (1 + sqrt(3))^n * 2^(n*(n-3)/2), where c = 0.9296543230172164460137009343716233391546324099495685771220234877636263909188... - _Vaclav Kotesovec_, Jul 03 2025
%e A195067 G.f.: A(x) = 1 + x + 3*x^2 + 17*x^3 + 191*x^4 + 4261*x^5 +...
%e A195067 where:
%e A195067 A(x) = 1 + x*A(2*x) + x^2*A(4*x) + x^3*A(6*x) + x^4*A(8*x) + x^5*A(10*x) +...
%t A195067 a[0] = 1; a[n_] := a[n] = Sum[2^k * (n-k)^k * a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 03 2025 *)
%o A195067 (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*subst(A,x,2*j*x))); polcoeff(A, n)}
%o A195067 (PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, 2^k*(n-k)^k*a(k)))}
%Y A195067 Cf. A125282, A385546.
%K A195067 nonn
%O A195067 0,3
%A A195067 _Paul D. Hanna_, Sep 08 2011