A349034 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(-4*x)).

1, 2, -4, -88, 5360, 1395104, -1423111744, -5834786588032, 95573832673124096, 6263909110244685920768, -1642021136070472933898232832, -1721790522986063937046243536001024, 7221705990593287793620261453916626546688, 121160150179535955805047509278599956409746825216

Offset: 0

Author

Ilya Gutkovskiy, Nov 06 2021

Keywords

• sign

Crossrefs

Cf. A006318, A015099, A348877, A349032, A349033.

Programs

Mathematica

nmax = 13; A[] = 0; Do[A[x] = 1/(1 - x - 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[(-4)^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]

Formula

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