A353605 Product_{n>=1} (1 + a(n)*x^n) = 1 + Sum_{n>=1} prime(n+1)*x^n.

3, 5, -8, 35, -52, 118, -320, 1597, -2016, 6616, -16064, 40516, -122552, 381606, -903176, 4389807, -7597004, 22835416, -61172890, 188526110, -486889660, 1550995910, -4093173788, 11608277912, -33815484714, 105179650108, -279683446078, 883705997682, -2366564864546

Offset: 1

Author

Ilya Gutkovskiy, May 07 2022

Keywords

• sign

Crossrefs

Cf. A006005, A065091, A147557, A353606.

Programs

Mathematica

nn = 29; f[x_] := Product[(1 + a[n] x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - Sum[Prime[k + 1] x^k, {k, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten