A353911 Product_{n>=1} 1 / (1 - a(n)*x^n/n!) = 1 + tan(x).

1, -2, 2, -32, 56, -416, 3184, -85504, 309760, -4087552, 48104704, -546922496, 10591523840, -194387924992, 3133776259072, -129880886411264, 1249919350046720, -29073986250604544, 624022403933077504, -15137719350365519872, 381632216575339397120, -11149155036737662615552

Offset: 1

Author

Ilya Gutkovskiy, May 10 2022

Keywords

• sign

Crossrefs

Cf. A000182, A009006, A353583, A353584, A353611, A353873, A353910, A353912.

Programs

Mathematica

nn = 22; f[x_] := Product[1/(1 - a[n] x^n/n!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - 1 - Tan[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten