A171192 G.f. satisfies A(x) = 1/(1 - x*A(2x)^2).
1, 1, 5, 53, 1045, 37941, 2596693, 343615093, 89402126741, 46139256172725, 47433024462021589, 97333484052884523765, 399068205440018335950357, 3270764880283567936326235445, 53601302478763156422575938811989
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..81
Programs
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Mathematica
nmax = 15; A[] = 0; Do[A[x] = 1/(1 - x*A[2*x]^2) + 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)^2) ); polcoeff(A, n)}
Formula
a(0) = 1; a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-1} 2^(i+j) * a(i) * a(j) * a(n-i-j-1). - Ilya Gutkovskiy, Nov 03 2021
a(n) ~ c * 2^(n*(n+1)/2), where c = 1.3216968146657309382653061124105846042506... - Vaclav Kotesovec, Nov 03 2021