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

1, 1, 4, 26, 216, 2091, 22532, 263302, 3282572, 43184125, 594892016, 8533187394, 126911650416, 1950679300314, 30905935176876, 503694878376602, 8429969774716104, 144679270141457684, 2543281262706638148, 45745868441595695376, 841201149601799641988, 15801799739741607604585

Offset: 0

Author

Paul D. Hanna, Aug 14 2008

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 26*x^3 + 216*x^4 + 2091*x^5 + 22532*x^6 +...
A(x*A(x)) = 1 + x + 5*x^2 + 38*x^3 + 356*x^4 + 3801*x^5 + 44508*x^6 +...
A(x*A(x))^4 = 1 + 4*x + 26*x^2 + 216*x^3 + 2091*x^4 + 22532*x^5 +...
		

Crossrefs

Cf. A143426, A143435, A143437.

Programs

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)}

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

Formula

G.f. satisfies: x - G(x) = G(x)^2*A(x)^4 where G(x*A(x)) = x.

From Seiichi Manyama, Jun 05 2025: (Start)

Let a(n,k) = [x^n] A(x)^k.

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)