A346059 G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)) / (1 - x)^4.

1, -1, -3, -2, 15, 62, 56, -566, -3318, -6241, 33022, 330939, 1211873, -1330691, -47459905, -310788796, -675462411, 7151217040, 93213242926, 515144576280, 122725585740, -27551616750331, -296570472858772, -1477869678576483, 3416889475636695, 146832017085068163, 1522825949942199537

Offset: 0

Author

Ilya Gutkovskiy, Jul 03 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..592

Crossrefs

Cf. A000587, A014619, A045499, A346053, A346060.

Programs

Mathematica

nmax = 26; A[] = 0; Do[A[x] = 1 - x A[x/(1 - x)]/(1 - x)^4 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n + 2, k + 3] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 26}]

Formula

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