A171210 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^8.

1, 1, 16, 624, 47552, 6804576, 1849952000, 975746615040, 1013611906401280, 2090459909088346368, 8592166589474459877376, 70508055994868618069409792, 1156194054760373598022278840320, 37902377449956182566891283844956160, 2484501232375923934830943089632156319744

Offset: 0

Author

Paul D. Hanna, Dec 05 2009

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..79

Crossrefs

Cf. A135867, A171200-A171209, A171211, A343439.

Cf. A171197.

Programs

Mathematica

terms = 15; A[] = 0; Do[A[x] = 1+x*A[2x]^8 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)

PARI

{a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^8); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_8>=0 and x_1+x_2+...+x_8=n-1} Product_{k=1..8} a(x_k). - Seiichi Manyama, Jul 08 2025