A354175 - OEIS

%I #6 May 22 2022 08:54:54

%S 1,0,2,-8,56,-256,3184,-36224,273920,-2845696,48104704,-676312064,

%T 10591523840,-149454094336,2888557717504,-72214957359104,

%U 1249919350046720,-23620669488234496,624022403933077504,-15637185047733469184,372737701735949926400,-9655667879651150135296

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

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

%t 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}]

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

%K sign

%O 1,3

%A _Ilya Gutkovskiy_, May 18 2022