A348902 G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(4*x)).

1, 1, 9, 305, 39705, 20412737, 41846783913, 342892875489361, 11236600170415809849, 1472826135905484728387681, 772188014962631262957890704329, 1619397184353040716422147490531778929, 13584491414647344530078887450781292845554521

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Formula

a(0) = 1; a(n) = -a(n-1) + Sum_{k=0..n-1} 2^(2*k+1) * a(k) * a(n-k-1).

a(n) ~ c * 2^(n^2), where c = 2^(7/8) / EllipticTheta(2, 0, 1/sqrt(2)) = 0.6091497110662286155211146043057245512950999410185846745870491125003511... (same constant as in A165941). - Vaclav Kotesovec, Nov 03 2021, updated Apr 21 2024

Mathematica

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

Crossrefs

Cf. A001003, A015085, A165941, A348188, A348901.

Sequence in context: A196694 A196727 A197067 * A279449 A152437 A296802

Adjacent sequences: A348899 A348900 A348901 * A348903 A348904 A348905

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 03 2021

Status

approved