A354175 Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + tan(x).

1, 0, 2, -8, 56, -256, 3184, -36224, 273920, -2845696, 48104704, -676312064, 10591523840, -149454094336, 2888557717504, -72214957359104, 1249919350046720, -23620669488234496, 624022403933077504, -15637185047733469184, 372737701735949926400, -9655667879651150135296

Offset: 1

Author

Ilya Gutkovskiy, May 18 2022

Keywords

• sign

Crossrefs

Cf. A000182, A009006, A067856, A353583, A353584, A353611, A353911, A354065, A354171, A354172, A354173, A354174, A354176.

Programs

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[c[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; c[n_] := c[n] = 2^(n + 1) (2^(n + 1) - 1) Abs[BernoulliB[n + 1]]/((n + 1) n!) - b[n, n - 1]; a[n_] := n! c[n]; Table[a[n], {n, 1, 22}]

Formula

E.g.f.: Sum_{k>=1} A067856(k) * log(1 + tan(x^k)) / k.