A353156 a(0) = 1; a(n) = -Sum_{k=1..n} prime(k+1) * a(n-k).

1, -3, 4, -4, 2, 6, -22, 46, -74, 86, -40, -120, 450, -958, 1506, -1694, 744, 2500, -9184, 19422, -30450, 34032, -14178, -52286, 188038, -394724, 615102, -681110, 268666, 1089974, -3847390, 8021030, -12426638, 13632728, -5063588, -22711916, 78708912, -162966020, 251005706

Offset: 0

Author

Ilya Gutkovskiy, Apr 27 2022

Keywords

• sign

Crossrefs

Cf. A006005, A030017, A030018, A065091, A292744, A300662, A307898, A307899, A346792.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = -Sum[Prime[k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 38}]
nmax = 38; CoefficientList[Series[1/(1 + Sum[Prime[k + 1] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1 / (1 + Sum_{k>=1} prime(k+1) * x^k).