A171200 G.f. satisfies A(x) = 1 + x*A(2x)^3.

1, 1, 6, 84, 2312, 121056, 12173568, 2391143424, 928316362752, 716762538541056, 1103851068987015168, 3395472896229407981568, 20875407961847891162038272, 256600638160251032545689337856, 6307244441266548036155317187248128

Offset: 0

Author

Paul D. Hanna, Dec 05 2009

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A135867, A171201, A171202-A171211, A343439.

Programs

Mathematica

m = 15; A[] = 0; Do[A[x] = 1 + x A[2x]^3 + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Nov 07 2019 *)

PARI

{a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^3); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{i=0..n-1} Sum_{j=0..n-i-1} a(i) * a(j) * a(n-i-j-1). - Ilya Gutkovskiy, Nov 03 2021