A171196 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^6).

1, 1, 13, 397, 23261, 2532093, 520285021, 206632208765, 161306955003037, 249753449538341821, 770275887324912000733, 4741871606773351738426877, 58325180751309642789169099037, 1434100517517383561901937569640509

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. A015083, A171192-A171195, A171197, A171198.

Programs

Mathematica

nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^6) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 03 2021 *)

PARI

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

Formula

a(n) ~ c * 2^(n*(n+1)/2) * 3^n, where c = 0.363484431362432363073577975298028185297326... - Vaclav Kotesovec, Nov 03 2021

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_7>=0 and x_1+x_2+...+x_7=n-1} (1/2)^x_1 * Product_{k=1..7} a(x_k). - Seiichi Manyama, Jul 06 2025