A349033 G.f. A(x) satisfies: A(x) = 1 / (1 - x - x * A(-3*x)).

1, 2, -2, -34, 826, 70634, -16895162, -12385295242, 27037369868722, 177500531682526034, -3493033395457140741746, -206274103942288894158940594, 36540013650535335202759969693162, 19419007557809179132528500713950083002, -30960092711143410415029705970483650552421802

Offset: 0

Author

Ilya Gutkovskiy, Nov 06 2021

Keywords

• sign

Crossrefs

Cf. A006318, A015098, A348876, A349032, A349034.

Programs

Mathematica

nmax = 14; A[] = 0; Do[A[x] = 1/(1 - x - x A[-3 x]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = a[n - 1] + Sum[(-3)^k a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 14}]

Formula

a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (-3)^k * a(k) * a(n-k-1).