A337514 G.f. A(x) satisfies: A(x) = 1 - Sum_{k=1..5} (x * A(x))^k.

1, -1, 0, 1, 0, -2, 1, -1, 13, -16, -39, 76, 122, -365, -64, 537, 1103, -1565, -6850, 6630, 38704, -58273, -108054, 204722, 366920, -598506, -1526994, 1111475, 9656314, -7254090, -43224847, 39704799, 171028427, -177129071, -604754108

Offset: 0

Author

Ilya Gutkovskiy, Aug 30 2020

Keywords

• sign

Crossrefs

Cf. A001591, A007440, A036767, A337512, A337513.

Programs

Mathematica

nmax = 34; A[] = 0; Do[A[x] = 1 - Sum[(x A[x])^k, {k, 1, 5}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
nmax = 35; CoefficientList[(1/x) InverseSeries[Series[x/(1 - x - x^2 - x^3 - x^4 - x^5), {x, 0, nmax}], x], x]
b[m_, r_, k_] := b[m, r, k] = If[m + r == 0, 1, Sum[b[m - j, r + j - 1, k], {j, 1, Min[1, m]}] - Sum[b[m + j - 1, r - j, k], {j, 1, Min[k, r]}]]; a[n_] := b[0, n, 5]; Table[a[n], {n, 0, 34}]

Formula

G.f.: A(x) = (1/x) * Series_Reversion(x / (1 - x - x^2 - x^3 - x^4 - x^5)).