A346060 G.f. A(x) satisfies: A(x) = 1 - x * A(x/(1 - x)) / (1 - x)^5.

1, -1, -4, -5, 19, 119, 226, -789, -7747, -25333, 29428, 826059, 4651651, 7008499, -108045466, -1124213961, -4968432059, 6515205811, 300350438716, 2561696929271, 9034737779711, -58377397309001, -1213955186657474, -9784487206914505, -27228229386096731, 417997375131879519

Offset: 0

Author

Ilya Gutkovskiy, Jul 03 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..591

Crossrefs

Cf. A000587, A014619, A045500, A346053, A346059.

Programs

Mathematica

nmax = 25; A[] = 0; Do[A[x] = 1 - x A[x/(1 - x)]/(1 - x)^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n + 3, k + 4] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 25}]

Formula

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