A349037 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x^2 * A(-4*x)).

1, 1, 2, -1, 29, 116, 7701, -103563, 31343898, 1759289595, 2057705197793, -457070362176172, 2156748187140412361, 1921405067209313680505, 36188075164863127910696914, -128870933294125665748520896793, 9713904752944734908048841134573557

Offset: 0

Author

Ilya Gutkovskiy, Nov 06 2021

Keywords

• sign

Crossrefs

Cf. A001006, A015099, A348880, A349035, A349036.

Programs

Mathematica

nmax = 16; A[] = 0; Do[A[x] = 1/(1 - x - x^2 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[(-4)^k a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 16}]

Formula

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