A349287 G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(4*x)^2).

1, 1, 9, 321, 42937, 22259313, 45726174057, 374866565186721, 12285883413435994137, 1610409077693221284887505, 844327818646575560326075164105, 1770688839714867344554954935264852993, 14853625190589908388648838739441430566681721

Offset: 0

Author

Ilya Gutkovskiy, Nov 13 2021

Keywords

• nonn

Crossrefs

Cf. A001764, A015085, A171192, A349286.

Programs

Mathematica

nmax = 12; A[] = 0; Do[A[x] = 1/(1 - x A[4 x]^2) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Sum[4^(i + j) a[i] a[j] a[n - i - j - 1], {j, 0, n - i - 1}], {i, 0, n - 1}]; Table[a[n], {n, 0, 12}]

Formula

a(0) = 1; a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-1} 4^(i+j) * a(i) * a(j) * a(n-i-j-1).

a(n) ~ c * 2^(n^2), where c = 0.6660597482166910709619924328518595274303795046... - Vaclav Kotesovec, Nov 14 2021