A349046 G.f. A(x) satisfies: A(x) = 1 / (1 + x - 2 * x * A(-4*x)).

1, 1, -7, -239, 30185, 15518977, -31752293287, -260178568173071, 8525011498792301513, 1117407361630407158712289, -585841036144574163016069731271, -1228598872333737909217248906305521967, 10306231872061986643099600924851012311829929

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = -a(n-1) + 2 * Sum_{k=0..n-1} (-4)^k * a(k) * a(n-k-1).

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] + 2 Sum[(-4)^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 12}]

Crossrefs

Cf. A001003, A015099, A348902, A349038, A349045.

Sequence in context: A366703 A185389 A159967 * A139057 A251594 A210248

Adjacent sequences: A349043 A349044 A349045 * A349047 A349048 A349049

Keyword

sign

Author

Ilya Gutkovskiy, Nov 06 2021

Status

approved