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A171206

G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^6.

1, 1, 12, 348, 19744, 2108784, 428817600, 169398274624, 131889504749568, 203937600707475456, 628561895904796999680, 3868208404121906515820544, 47571342639450113377565933568, 1169589733863427138021074362433536, 57499379103783344787572704263568097280, 5652994168279651703590653986228287051923456

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OFFSET

0,3

LINKS

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

FORMULA

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_6>=0 and x_1+x_2+...+x_6=n-1} Product_{k=1..6} a(x_k). - Seiichi Manyama, Jul 08 2025

MATHEMATICA

terms = 16; A[_] = 0; Do[A[x_] = 1+x*A[2x]^6 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)

PROG

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^6); polcoeff(A, n)}

CROSSREFS