A354276 Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + arctanh(x).

1, 0, 2, -8, 64, -304, 3968, -43392, 378880, -4002816, 68247552, -995736576, 15949529088, -238273241088, 4760383438848, -113132156780544, 2119956936523776, -42743492966350848, 1123874181449515008, -28901050300546154496, 722523072906903158784, -19401957422023594475520, 589068777481530305937408

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Formula

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

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] = Mod[n, 2]/n - b[n, n - 1]; a[n_] := n! c[n]; Table[a[n], {n, 1, 23}]

Crossrefs

Cf. A010050, A067856, A353821, A353928, A353972, A354118, A354176, A354274, A354275.

Sequence in context: A295232 A287229 A323853 * A353821 A354237 A191570

Adjacent sequences: A354273 A354274 A354275 * A354277 A354278 A354279

Keyword

sign

Author

Ilya Gutkovskiy, May 22 2022

Status

approved