A171195 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^5).

1, 1, 11, 281, 13731, 1245601, 213268203, 70580511385, 45914883339027, 59241954299963729, 152258885235304955131, 781096727709105092232777, 8006263111571482684378716067, 164048440920655457493139473502081

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-A171194, A171196-A171198.

Programs

Mathematica

nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^5) + 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)^5) ); polcoeff(A, n)}

Formula

a(n) ~ c * 2^(n*(n-1)/2) * 5^n, where c = 0.444871440417987089861554304425221691031547... - Vaclav Kotesovec, Nov 03 2021

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} (1/2)^x_1 * Product_{k=1..6} a(x_k). - Seiichi Manyama, Jul 06 2025