A396263 G.f. A(x) satisfies: A(x) = 1 + x * A(2*x)^2 / (1 - x).

1, 1, 5, 49, 913, 32097, 2160417, 283540193, 73475433185, 37844619113441, 38867563569600481, 79717929470859158497, 326764349731472893461473, 2677834974477935233005523937, 43881686326238030953299581260769, 1438046780187215577831515887315227617

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

a(0) = 1, for n > 0: a(n) = Sum_{j=0..n-1} Sum_{i=0..j} 2^j * a(i) * a(j-i).

a(n) ~ c * 2^(n*(n+1)/2), where c = 1.08196521469192597073952596757584721975493255637537195949... - Vaclav Kotesovec, May 26 2026

Mathematica

nmax = 15; A[_] = 0; Do[A[x_] = 1 + x A[2 x]^2/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
(* Alternative: *)
a[0] = 1; a[n_] := a[n] = Sum[Sum[2^j a[i] a[j - i], {i, 0, j}], {j, 0, n - 1}]; Table[a[n], {n, 0, 15}]

Crossrefs

Cf. A002212, A015083, A028362, A135867.

Sequence in context: A064618 A249588 A348901 * A363480 A193199 A224680

Adjacent sequences: A396260 A396261 A396262 * A396264 A396265 A396266

Keyword

nonn

Author

Ilya Gutkovskiy, May 20 2026

Status

approved