A353606 Product_{n>=1} (1 + a(n)*x^n) = 1 + x + Sum_{n>=2} prime(n-1)*x^n.

1, 2, 1, 4, 1, 0, -1, 11, -3, -7, 4, -10, 5, -15, -4, 151, -9, -50, -3, -63, 19, -176, 6, 591, -27, -637, 13, -999, 50, -1957, -49, 27250, -162, -7887, 83, -12821, 468, -27226, -40, 127341, -1215, -99166, -526, -174140, 2640, -362870, 1673, 1419061, -4516, -1344620

Offset: 1

Author

Ilya Gutkovskiy, May 07 2022

Keywords

• sign

Crossrefs

Cf. A008578, A147557, A353605.

Programs

Mathematica

nn = 50; f[x_] := Product[(1 + a[n] x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - x - Sum[Prime[k - 1] x^k, {k, 2, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten