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

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..81

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

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 *)

Prog

(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)}

Crossrefs

Cf. A015083, A171193-A171198.

Sequence in context: A128943 A180351 A337151 * A330435 A113068 A099086

Adjacent sequences: A171189 A171190 A171191 * A171193 A171194 A171195

Keyword

nonn

Author

Paul D. Hanna, Dec 05 2009

Status

approved