A171198 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^8).
1, 1, 17, 689, 53777, 7805201, 2138582801, 1132509669905, 1178804946216209, 2433551908785577745, 10007244528797884954897, 82140401194398306308608785, 1347106337625031145913841134865, 44163564651481078406730693648713489
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..79
Programs
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Mathematica
nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^8) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 03 2021 *)
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PARI
{a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1/(1-x*subst(A, x, 2*x)^8) ); polcoeff(A, n)}
Formula
a(n) ~ c * 2^(n*(n+5)/2), where c = 0.265929653305627916979803234586945454418485... - Vaclav Kotesovec, Nov 03 2021
a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_9>=0 and x_1+x_2+...+x_9=n-1} (1/2)^x_1 * Product_{k=1..9} a(x_k). - Seiichi Manyama, Jul 06 2025