A171193 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^3).
1, 1, 7, 109, 3207, 174581, 17929279, 3559607005, 1389312382199, 1075527698708485, 1658535837898129263, 5105026337441341642861, 31395991691829167745766311, 385982564381552315528268500501
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..80
Programs
-
Mathematica
nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^3) + 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)^3) ); polcoeff(A, n)}
Formula
a(n) ~ c * 2^(n*(n-1)/2) * 3^n, where c = 0.80142677004566734464115933731029720165641... - Vaclav Kotesovec, Nov 03 2021
a(0) = 1; a(n) = 2^(n-1) * Sum_{i, j, k, l>=0 and i+j+k+l=n-1} (1/2)^i * a(i) * a(j) * a(k) * a(l). - Seiichi Manyama, Jul 06 2025