A353611 Product_{n>=1} (1 + a(n)*x^n/n!) = 1 + tan(x).

1, 0, 2, -8, 56, -336, 3184, -27264, 309760, -3297280, 48104704, -624745472, 10591523840, -159594803200, 3133776259072, -56224864108544, 1249919350046720, -24600643845095424, 624022403933077504, -14094091678163140608, 381632216575339397120, -9516741266133420605440

Offset: 1

Author

Ilya Gutkovskiy, May 07 2022

Keywords

• sign

Crossrefs

Cf. A000182, A006973, A009006, A137852, A353583, A353584, A353607, A353608, A353609, A353610.

Programs

Mathematica

nn = 22; f[x_] := Product[(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