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A143436 G.f. A(x) satisfies A(x) = 1 + x*A(x*A(x))^4.

%I A143436 #7 Jun 05 2025 09:52:22
%S A143436 1,1,4,26,216,2091,22532,263302,3282572,43184125,594892016,8533187394,
%T A143436 126911650416,1950679300314,30905935176876,503694878376602,
%U A143436 8429969774716104,144679270141457684,2543281262706638148,45745868441595695376,841201149601799641988,15801799739741607604585
%N A143436 G.f. A(x) satisfies A(x) = 1 + x*A(x*A(x))^4.
%F A143436 G.f. satisfies: x - G(x) = G(x)^2*A(x)^4 where G(x*A(x)) = x.
%F A143436 From _Seiichi Manyama_, Jun 05 2025: (Start)
%F A143436 Let a(n,k) = [x^n] A(x)^k.
%F A143436 a(n,0) = 0^n; a(n,k) = k * Sum_{j=0..n} binomial(n-j+k,j)/(n-j+k) * a(n-j,4*j). (End)
%e A143436 G.f.: A(x) = 1 + x + 4*x^2 + 26*x^3 + 216*x^4 + 2091*x^5 + 22532*x^6 +...
%e A143436 A(x*A(x)) = 1 + x + 5*x^2 + 38*x^3 + 356*x^4 + 3801*x^5 + 44508*x^6 +...
%e A143436 A(x*A(x))^4 = 1 + 4*x + 26*x^2 + 216*x^3 + 2091*x^4 + 22532*x^5 +...
%o A143436 (PARI) {a(n)=local(A=1+x+x*O(x^n));for(i=0,n,A=1+x*subst(A^4,x,x*A));polcoeff(A,n)}
%o A143436 (PARI) a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(n-j+k, j)/(n-j+k)*a(n-j, 4*j))); \\ _Seiichi Manyama_, Jun 05 2025
%Y A143436 Cf. A143426, A143435, A143437.
%K A143436 nonn
%O A143436 0,3
%A A143436 _Paul D. Hanna_, Aug 14 2008